1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
|
<!DOCTYPE html>
<html lang="en" data-content_root="../" >
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Summary of Sparse Linear Solvers Available In PETSc — PETSc 3.23.1 documentation</title>
<script data-cfasync="false">
document.documentElement.dataset.mode = localStorage.getItem("mode") || "";
document.documentElement.dataset.theme = localStorage.getItem("theme") || "light";
</script>
<!-- Loaded before other Sphinx assets -->
<link href="../_static/styles/theme.css?digest=bd9e20870c6007c4c509" rel="stylesheet" />
<link href="../_static/styles/bootstrap.css?digest=bd9e20870c6007c4c509" rel="stylesheet" />
<link href="../_static/styles/pydata-sphinx-theme.css?digest=bd9e20870c6007c4c509" rel="stylesheet" />
<link href="../_static/vendor/fontawesome/6.5.1/css/all.min.css?digest=bd9e20870c6007c4c509" rel="stylesheet" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.5.1/webfonts/fa-solid-900.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.5.1/webfonts/fa-brands-400.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.5.1/webfonts/fa-regular-400.woff2" />
<link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=8f2a1f02" />
<link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
<link rel="stylesheet" type="text/css" href="../_static/sphinx-design.min.css?v=87e54e7c" />
<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/katex.min.css" />
<link rel="stylesheet" type="text/css" href="../_static/katex-math.css?v=91adb8b6" />
<link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=dbe1606d" />
<!-- Pre-loaded scripts that we'll load fully later -->
<link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=bd9e20870c6007c4c509" />
<link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=bd9e20870c6007c4c509" />
<script src="../_static/vendor/fontawesome/6.5.1/js/all.min.js?digest=bd9e20870c6007c4c509"></script>
<script src="../_static/documentation_options.js?v=34da53a5"></script>
<script src="../_static/doctools.js?v=9a2dae69"></script>
<script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
<script src="../_static/clipboard.min.js?v=a7894cd8"></script>
<script src="../_static/copybutton.js?v=a56c686a"></script>
<script src="../_static/design-tabs.js?v=f930bc37"></script>
<script src="../_static/katex.min.js?v=be8ff15f"></script>
<script src="../_static/auto-render.min.js?v=ad136472"></script>
<script src="../_static/katex_autorenderer.js?v=bebc588a"></script>
<script>DOCUMENTATION_OPTIONS.pagename = 'overview/linear_solve_table';</script>
<link rel="icon" href="../_static/petsc_favicon.png"/>
<link rel="index" title="Index" href="../genindex.html" />
<link rel="search" title="Search" href="../search.html" />
<link rel="next" title="Summary of Nonlinear Solvers Available In PETSc" href="nonlinear_solve_table.html" />
<link rel="prev" title="Summary of Matrix Types Available In PETSc" href="matrix_table.html" />
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
<meta name="docbuild:last-update" content="2025-04-30T13:10:40-0500 (v3.23.1)"/>
</head>
<body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="">
<a id="pst-skip-link" class="skip-link" href="#main-content">Skip to main content</a>
<div id="pst-scroll-pixel-helper"></div>
<button type="button" class="btn rounded-pill" id="pst-back-to-top">
<i class="fa-solid fa-arrow-up"></i>
Back to top
</button>
<input type="checkbox"
class="sidebar-toggle"
name="__primary"
id="__primary"/>
<label class="overlay overlay-primary" for="__primary"></label>
<input type="checkbox"
class="sidebar-toggle"
name="__secondary"
id="__secondary"/>
<label class="overlay overlay-secondary" for="__secondary"></label>
<div class="search-button__wrapper">
<div class="search-button__overlay"></div>
<div class="search-button__search-container">
<form class="bd-search d-flex align-items-center"
action="../search.html"
method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search"
class="form-control"
name="q"
id="search-input"
placeholder="Search the docs ..."
aria-label="Search the docs ..."
autocomplete="off"
autocorrect="off"
autocapitalize="off"
spellcheck="false"/>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form></div>
</div>
<header>
<div class="bd-header navbar navbar-expand-lg bd-navbar">
<div class="bd-header__inner bd-page-width">
<label class="sidebar-toggle primary-toggle" for="__primary">
<span class="fa-solid fa-bars"></span>
</label>
<div class="col-lg-3 navbar-header-items__start">
<div class="navbar-item">
<a class="navbar-brand logo" href="../index.html">
<img src="../_static/PETSc-TAO_RGB.svg" class="logo__image only-light" alt="PETSc 3.23.1 documentation - Home"/>
<script>document.write(`<img src="../_static/PETSc-TAO_RGB_white.svg" class="logo__image only-dark" alt="PETSc 3.23.1 documentation - Home"/>`);</script>
</a></div>
</div>
<div class="col-lg-9 navbar-header-items">
<div class="me-auto navbar-header-items__center">
<div class="navbar-item">
<nav class="navbar-nav">
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item current active">
<a class="nav-link nav-internal" href="index.html">
Overview
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../install/index.html">
Install
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../tutorials/index.html">
Tutorials
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../manual/index.html">
User-Guide
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../manualpages/index.html">
C/Fortran API
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../petsc4py/index.html">
petsc4py API
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../faq/index.html">
FAQ
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../community/index.html">
Community
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../developers/index.html">
Developers
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../miscellaneous/index.html">
Misc.
</a>
</li>
</ul>
</nav></div>
</div>
<div class="navbar-header-items__end">
<div class="navbar-item navbar-persistent--container">
<script>
document.write(`
<button class="btn navbar-btn search-button-field search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass"></i>
<span class="search-button__default-text">Search</span>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd class="kbd-shortcut__modifier">K</kbd></span>
</button>
`);
</script>
</div>
<div class="navbar-item">
<script>
document.write(`
<button class="btn btn-sm navbar-btn theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
<span class="theme-switch nav-link" data-mode="light"><i class="fa-solid fa-sun fa-lg"></i></span>
<span class="theme-switch nav-link" data-mode="dark"><i class="fa-solid fa-moon fa-lg"></i></span>
<span class="theme-switch nav-link" data-mode="auto"><i class="fa-solid fa-circle-half-stroke fa-lg"></i></span>
</button>
`);
</script></div>
<div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://gitlab.com/petsc/petsc" title="GitLab" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fab fa-gitlab fa-lg" aria-hidden="true"></i></span>
<span class="sr-only">GitLab</span></a>
</li>
</ul></div>
</div>
</div>
<div class="navbar-persistent--mobile">
<script>
document.write(`
<button class="btn navbar-btn search-button-field search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass"></i>
<span class="search-button__default-text">Search</span>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd class="kbd-shortcut__modifier">K</kbd></span>
</button>
`);
</script>
</div>
<label class="sidebar-toggle secondary-toggle" for="__secondary" tabindex="0">
<span class="fa-solid fa-outdent"></span>
</label>
</div>
</div>
</header>
<div class="bd-container">
<div class="bd-container__inner bd-page-width">
<div class="bd-sidebar-primary bd-sidebar">
<div class="sidebar-header-items sidebar-primary__section">
<div class="sidebar-header-items__center">
<div class="navbar-item">
<nav class="navbar-nav">
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item current active">
<a class="nav-link nav-internal" href="index.html">
Overview
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../install/index.html">
Install
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../tutorials/index.html">
Tutorials
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../manual/index.html">
User-Guide
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../manualpages/index.html">
C/Fortran API
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../petsc4py/index.html">
petsc4py API
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../faq/index.html">
FAQ
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../community/index.html">
Community
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../developers/index.html">
Developers
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../miscellaneous/index.html">
Misc.
</a>
</li>
</ul>
</nav></div>
</div>
<div class="sidebar-header-items__end">
<div class="navbar-item">
<script>
document.write(`
<button class="btn btn-sm navbar-btn theme-switch-button" title="light/dark" aria-label="light/dark" data-bs-placement="bottom" data-bs-toggle="tooltip">
<span class="theme-switch nav-link" data-mode="light"><i class="fa-solid fa-sun fa-lg"></i></span>
<span class="theme-switch nav-link" data-mode="dark"><i class="fa-solid fa-moon fa-lg"></i></span>
<span class="theme-switch nav-link" data-mode="auto"><i class="fa-solid fa-circle-half-stroke fa-lg"></i></span>
</button>
`);
</script></div>
<div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://gitlab.com/petsc/petsc" title="GitLab" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fab fa-gitlab fa-lg" aria-hidden="true"></i></span>
<span class="sr-only">GitLab</span></a>
</li>
</ul></div>
</div>
</div>
<div class="sidebar-primary-items__start sidebar-primary__section">
<div class="sidebar-primary-item">
<nav class="bd-docs-nav bd-links"
aria-label="Section Navigation">
<p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
<div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="nutshell.html">PETSc in a nutshell</a></li>
<li class="toctree-l1"><a class="reference internal" href="features.html">Supported Systems</a></li>
<li class="toctree-l1"><a class="reference internal" href="gpu_roadmap.html">GPU Support Roadmap</a></li>
<li class="toctree-l1"><a class="reference internal" href="vector_table.html">Summary of Vector Types Available In PETSc</a></li>
<li class="toctree-l1"><a class="reference internal" href="matrix_table.html">Summary of Matrix Types Available In PETSc</a></li>
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Summary of Sparse Linear Solvers Available In PETSc</a></li>
<li class="toctree-l1"><a class="reference internal" href="nonlinear_solve_table.html">Summary of Nonlinear Solvers Available In PETSc</a></li>
<li class="toctree-l1"><a class="reference internal" href="integrator_table.html">Summary of Time Integrators Available In PETSc</a></li>
<li class="toctree-l1"><a class="reference internal" href="tao_solve_table.html">Summary of Tao Solvers</a></li>
<li class="toctree-l1"><a class="reference internal" href="discrete_table.html">Summary of Discretization Management Systems</a></li>
<li class="toctree-l1"><a class="reference internal" href="plex_transform_table.html">Summary of Unstructured Mesh Transformations</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../manual/index.html">User-Guide</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manual/introduction.html">Introduction to PETSc</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manual/about_this_manual.html">About This Manual</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/getting_started.html">Getting Started</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manual/programming.html">The Solvers in PETSc/TAO</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manual/vec.html">Vectors and Parallel Data</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/mat.html">Matrices</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/ksp.html">KSP: Linear System Solvers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/snes.html">SNES: Nonlinear Solvers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/ts.html">TS: Scalable ODE and DAE Solvers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/tao.html">TAO: Optimization Solvers</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manual/dm.html">DM: Interfacing Between Solvers and Models/Discretizations</a><input class="toctree-checkbox" id="toctree-checkbox-4" name="toctree-checkbox-4" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-4"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manual/dmbase.html">DM Basics</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/section.html">PetscSection: Connecting Grids to Data</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/dmplex.html">DMPlex: Unstructured Grids</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/dmstag.html">DMSTAG: Staggered, Structured Grid</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/dmnetwork.html">Networks</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/dt.html">PetscDT: Discretization Technology in PETSc</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/fe.html">PetscFE: Finite Element Infrastructure in PETSc</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manual/additional.html">Additional Information</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-5"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manual/fortran.html">PETSc for Fortran Users</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/versionchecking.html">Checking the PETSc version</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/matlab.html">Using MATLAB with PETSc</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/profiling.html">Profiling</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/performance.html">Hints for Performance Tuning</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/streams.html">STREAMS: Example Study</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/blas-lapack.html">The Use of BLAS and LAPACK in PETSc and external libraries</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/other.html">Other PETSc Features</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/advanced.html">Advanced Features of Matrices and Solvers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manual/tests.html">Running PETSc Tests</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1 has-children"><a class="reference internal" href="../manualpages/index.html">C/Fortran API</a><input class="toctree-checkbox" id="toctree-checkbox-6" name="toctree-checkbox-6" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-6"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/Vector.html">Vectors and Index Sets</a><input class="toctree-checkbox" id="toctree-checkbox-7" name="toctree-checkbox-7" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-7"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Vec/index.html">Vector Operations (Vec)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/IS/index.html">Index sets (IS)</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/Matrix.html">Matrices and Matrix Operations</a><input class="toctree-checkbox" id="toctree-checkbox-8" name="toctree-checkbox-8" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-8"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Mat/index.html">Matrix Operations (Mat)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/MatGraphOperations/index.html">Matrix colorings (MatColoring), orderings (MatOrdering), partitionings (MatPartitioning), and coarsening (MatCoarsen)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/MatFD/index.html">Finite difference computation of Jacobians (MatFD)</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/DataLayout.html">Data Layout and Communication</a><input class="toctree-checkbox" id="toctree-checkbox-9" name="toctree-checkbox-9" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-9"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/PetscSF/index.html">Star Forest Communication (PetscSF)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/PetscSection/index.html">Section Data Layout (PetscSection)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/AO/index.html">Application Orderings (AO)</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/DataManagement.html">Data Management between Vec and Mat, and Distributed Mesh Data Structures</a><input class="toctree-checkbox" id="toctree-checkbox-10" name="toctree-checkbox-10" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-10"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DM/index.html">Data Management (DM)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMDA/index.html">Structured Grids (DMDA)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMStag/index.html">Staggered, Structured Grids (DMSTAG)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMPlex/index.html">Unstructured Grids and Cell Complexes (DMPLEX)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMNetwork/index.html">Graphs and Networks (DMNETWORK)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMForest/index.html">A Forest of Trees and Structured Adaptive Refinement (DMFOREST)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMPatch/index.html">Sequences of parallel mesh patches (DMPATCH)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMSwarm/index.html">Particle Discretizations (DMSWARM)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMMOAB/index.html">MOAB Mesh Representation (DMMOAB)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMLabel/index.html">Selecting Parts of Meshes (DMLabel)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMPRODUCT/index.html">Tensor products of meshes (DMRODUCT)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DMComposite/index.html">DMComposite</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/Discretization.html">Discretization and Function Spaces</a><input class="toctree-checkbox" id="toctree-checkbox-11" name="toctree-checkbox-11" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-11"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DT/index.html">Discretization Technology and Quadrature (DT)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/SPACE/index.html">Function Spaces (PetscSpace)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/DUALSPACE/index.html">Dual Spaces (PetscDualSpace)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/FE/index.html">Finite Elements (PetscFE)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/FV/index.html">Finite Volumes (PetscFV)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/PF/index.html">Defining your own mathematical functions (PF)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/LANDAU/index.html">Landau Collision Operator</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/LinearSolvers.html">Linear Solvers and Preconditioners</a><input class="toctree-checkbox" id="toctree-checkbox-12" name="toctree-checkbox-12" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-12"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/KSP/index.html">Linear Solvers and Krylov Methods (KSP)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/PC/index.html">Preconditioners (PC)</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/NonlinearSolvers.html">Nonlinear Solvers</a><input class="toctree-checkbox" id="toctree-checkbox-13" name="toctree-checkbox-13" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-13"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/SNES/index.html">Nonlinear Solvers (SNES)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/SNESFAS/index.html">Full Approximation Scheme (FAS) nonlinear multigrid</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/Timestepping.html">Forward and Adjoint Timestepping</a><input class="toctree-checkbox" id="toctree-checkbox-14" name="toctree-checkbox-14" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-14"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/TS/index.html">Time Stepping ODE and DAE Solvers (TS)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Sensitivity/index.html">Sensitivity Analysis for ODE and DAE</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Characteristic/index.html">Semi-Lagrangian Solves using the Method of Characteristics</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/Optimization.html">Optimization</a><input class="toctree-checkbox" id="toctree-checkbox-15" name="toctree-checkbox-15" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-15"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Tao/index.html">Optimization Solvers (Tao)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/TaoLineSearch/index.html">Optimization Line Search (TaoLineSearch)</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/Visualization.html">Graphics and Visualization</a><input class="toctree-checkbox" id="toctree-checkbox-16" name="toctree-checkbox-16" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-16"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Draw/index.html">Graphics (Draw)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Viewer/index.html">Viewing Objects (Viewer)</a></li>
</ul>
</li>
<li class="toctree-l2 has-children"><a class="reference internal" href="../manualpages/System.html">System Routines, Profiling, Data Structures</a><input class="toctree-checkbox" id="toctree-checkbox-17" name="toctree-checkbox-17" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-17"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Sys/index.html">PETSc Options, IO, and System Utilities</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/PetscH/index.html">Hash Tables</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Log/index.html">Profiling and Logging</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Device/index.html">Device</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Matlab/index.html">Matlab</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/Bag/index.html">Bag</a></li>
<li class="toctree-l3"><a class="reference internal" href="../manualpages/BM/index.html">Benchmarks (BM)</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../changes/index.html">Changes for each release</a></li>
<li class="toctree-l2"><a class="reference internal" href="../manualpages/singleindex.html">Single Index of all PETSc Manual Pages</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../changes/index.html">Changes for each release</a></li>
<li class="toctree-l1"><a class="reference internal" href="../manualpages/singleindex.html">Single Index of all PETSc Manual Pages</a></li>
<li class="toctree-l1 has-children"><a class="reference internal" href="previous_release_docs.html">Documentation for previous PETSc releases</a><input class="toctree-checkbox" id="toctree-checkbox-18" name="toctree-checkbox-18" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-18"><i class="fa-solid fa-chevron-down"></i></label><ul>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.22/docs"> 3.22</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.21/docs"> 3.21</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.20/docs"> 3.20</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.19/docs"> 3.19</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.18/docs"> 3.18</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.17/docs"> 3.17</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.16/docs"> 3.16</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.15/docs"> 3.15</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.14/docs"> 3.14</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.13/docs"> 3.13</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.12/docs"> 3.12</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.11/docs"> 3.11</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.10/docs"> 3.10</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.9/docs"> 3.9</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.8/docs"> 3.8</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.7/docs"> 3.7</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.6/docs"> 3.6</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.5/docs"> 3.5</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.4/docs"> 3.4</a></li>
<li class="toctree-l2"><a class="reference external" href="https://web.cels.anl.gov/projects/petsc/vault/petsc-3.3/docs"> 3.3</a></li>
</ul>
</li>
</ul>
</div>
</nav></div>
</div>
<div class="sidebar-primary-items__end sidebar-primary__section">
</div>
<div id="rtd-footer-container"></div>
</div>
<main id="main-content" class="bd-main">
<div class="bd-content">
<div class="bd-article-container">
<div class="bd-header-article">
<div class="header-article-items header-article__inner">
<div class="header-article-items__start">
<div class="header-article-item">
<nav aria-label="Breadcrumb">
<ul class="bd-breadcrumbs">
<li class="breadcrumb-item breadcrumb-home">
<a href="../index.html" class="nav-link" aria-label="Home">
<i class="fa-solid fa-home"></i>
</a>
</li>
<li class="breadcrumb-item"><a href="index.html" class="nav-link">Overview</a></li>
<li class="breadcrumb-item active" aria-current="page">Summary of...</li>
</ul>
</nav>
</div>
</div>
</div>
</div>
<div id="searchbox"></div>
<article class="bd-article">
<section class="tex2jax_ignore mathjax_ignore" id="summary-of-sparse-linear-solvers-available-in-petsc">
<span id="doc-linsolve"></span><h1>Summary of Sparse Linear Solvers Available In PETSc<a class="headerlink" href="#summary-of-sparse-linear-solvers-available-in-petsc" title="Link to this heading">#</a></h1>
<section id="preconditioners">
<h2>Preconditioners<a class="headerlink" href="#preconditioners" title="Link to this heading">#</a></h2>
<table class="table table-center">
<thead>
<tr class="row-odd"><th class="head"></th>
<th class="head"><p>Algorithm</p></th>
<th class="head"><p>Associated Type</p></th>
<th class="head"><p>Matrix Types</p></th>
<th class="head"><p>External Packages</p></th>
<th class="head"><p>Parallel</p></th>
<th class="head"><p>Complex</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>Generic</p></td>
<td><p>Jacobi</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCJACOBI.html">PCJACOBI</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATDENSE.html">MATDENSE</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Point Block Jacobi</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCPBJACOBI.html">PCPBJACOBI</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATKAIJ.html">MATKAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATMPISELL.html">MATMPISELL</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATIS.html">MATIS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Variable Point Block Jacobi</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCPBJACOBI.html">PCPBJACOBI</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Block Jacobi</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCBJACOBI.html">PCBJACOBI</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>SOR</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCSOR.html">PCSOR</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQDENSE.html">MATSEQDENSE</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQSBAIJ.html">MATSEQSBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Point Block SOR</p></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQBAIJ.html">MATSEQBAIJ</a></span></code> (only for <code class="docutils notranslate"><span class="pre">bs</span></code> = 2,3,4,5)</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Kaczmarz</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCKACZMARZ.html">PCKACZMARZ</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Additive Schwarz</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCASM.html">PCASM</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Vanka/overlapping patches</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCPATCH.html">PCPATCH</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Deflation</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCDEFLATION.html">PCDEFLATION</a></span></code></p></td>
<td><p>All</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Incomplete</p></td>
<td><p>ILU</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCILU.html">PCILU</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQBAIJ.html">MATSEQBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>ILU with drop tolerance</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCILU.html">PCILU</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="../../manualpages/Mat/MATSOLVERSUPERLU.html">SuperLU Sequential ILU solver</a></p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCILU.html">PCILU</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>Euclid/hypre (<code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCHYPRE.html">PCHYPRE</a></span></code>)</p></td>
<td><p>X</p></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>ICholesky</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCICC.html">PCICC</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQBAIJ.html">MATSEQBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQSBAIJ.html">MATSEQSBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Algebraic recursive multilevel</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCPARMS.html">PCPARMS</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://www-users.cse.umn.edu/~saad/software/pARMS/">pARMS</a></p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Matrix Free</p></td>
<td><p>Infrastructure</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCSHELL.html">PCSHELL</a></span></code></p></td>
<td><p>All</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Multigrid</p></td>
<td><p>Infrastructure</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCMG.html">PCMG</a></span></code></p></td>
<td><p>All</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Geometric</p></td>
<td></td>
<td><p>All</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Smoothed Aggregation</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCGAMG.html">PCGAMG</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Smoothed Aggregation (ML)</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCML.html">PCML</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://trilinos.github.io/ml.html">ML/Trilinos</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Structured Geometric</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCPFMG.html">PCPFMG</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCSYSPFMG.html">PCSYSPFMG</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCSMG.html">PCSMG</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/DMDA/MATHYPRESTRUCT.html">MATHYPRESTRUCT</a></span></code></p></td>
<td><p><a class="reference external" href="https://hypre.readthedocs.io/en/latest/solvers-smg-pfmg.html">hypre</a></p></td>
<td><p>X</p></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Classical Algebraic</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCHYPRE.html">PCHYPRE</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCAMGX.html">PCAMGX</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://hypre.readthedocs.io/en/latest/solvers-boomeramg.html">BoomerAMG/hypre</a>, <a class="reference external" href="https://developer.nvidia.com/amgx">AmgX</a></p></td>
<td><p>X</p></td>
<td></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Multi-group MG</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCHMG.html">PCHMG</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Domain Decomposition</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCHPDDM.html">PCHPDDM</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATIS.html">MATIS</a></span></code></p></td>
<td><p><a class="reference external" href="https://github.com/hpddm/hpddm">HPDDM</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Hierarchical matrices</p></td>
<td><p><span class="math">\(\mathcal H^2\)</span></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCH2OPUS.html">PCH2OPUS</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATHTOOL.html">MATHTOOL</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATH2OPUS.html">MATH2OPUS</a></span></code></p></td>
<td><p><a class="reference external" href="https://github.com/ecrc/h2opus">H2OPUS</a></p></td>
<td><p>X</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>Physics-based Splitting</p></td>
<td><p>Relaxation & Schur Complement</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCFIELDSPLIT.html">PCFIELDSPLIT</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATNEST.html">MATNEST</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Galerkin composition</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCGALERKIN.html">PCGALERKIN</a></span></code></p></td>
<td><p>Any</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Additive/multiplicative</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCCOMPOSITE.html">PCCOMPOSITE</a></span></code></p></td>
<td><p>Any</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Least Squares Commutator</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCLSC.html">PCLSC</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/MATSCHURCOMPLEMENT.html">MATSCHURCOMPLEMENT</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Parallel transformation</p></td>
<td><p>Redistribution</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCREDISTRIBUTE.html">PCREDISTRIBUTE</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Telescoping communicator</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCTELESCOPE.html">PCTELESCOPE</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>Distribute for MPI</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCMPI.html">PCMPI</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Approximate Inverse</p></td>
<td><p>AIV</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCHYPRE.html">PCHYPRE</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCSPAI.html">PCSPAI</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://hypre.readthedocs.io/en/latest/solvers-parasails.html">Parasails/hypre</a>, <a class="reference external" href="https://epubs.siam.org/doi/abs/10.1137/S1064827595294691?journalCode=sjoce3">SPAI</a></p></td>
<td><p>X</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>Substructuring</p></td>
<td><p>Balancing Neumann-Neumann</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCNN.html">PCNN</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATIS.html">MATIS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Balancing Domain Decomposition</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCBDDC.html">PCBDDC</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATIS.html">MATIS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>2-level Schwarz wire basket</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCEXOTIC.html">PCEXOTIC</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
</tbody>
</table>
</section>
<hr class="docutils" />
<section id="direct-solvers">
<h2>Direct Solvers<a class="headerlink" href="#direct-solvers" title="Link to this heading">#</a></h2>
<table class="table table-center">
<thead>
<tr class="row-odd"><th class="head"></th>
<th class="head"><p>Algorithm</p></th>
<th class="head"><p>Associated Type</p></th>
<th class="head"><p>Matrix Types</p></th>
<th class="head"><p>External Packages</p></th>
<th class="head"><p>Parallel</p></th>
<th class="head"><p>Complex</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>Direct LU</p></td>
<td><p>LU</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCLU.html">PCLU</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQBAIJ.html">MATSEQBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://www.mathworks.com/products/matlab.html">MATLAB</a></p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="http://pastix.gforge.inria.fr/files/README-txt.html">PaStiX</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://portal.nersc.gov/project/sparse/superlu/">SuperLU</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATBAIJ.html">MATBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQSELL.html">MATSEQSELL</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATDENSE.html">MATDENSE</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATNEST.html">MATNEST</a></span></code></p></td>
<td><p><a class="reference external" href="https://mumps-solver.org/">MUMPS</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://www.ibm.com/support/knowledgecenter/en/SSFHY8/essl_welcome.html">ESSL</a></p></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://people.engr.tamu.edu/davis/suitesparse.html">UMFPACK (SuiteSparse)</a></p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://people.engr.tamu.edu/davis/suitesparse.html">KLU (SuiteSparse)</a></p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://web.stanford.edu/group/SOL/software/lusol/">LUSOL</a></p></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQBAIJ.html">MATSEQBAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html">MKL PARDISO</a></p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATMPIAIJ.html">MATMPIAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATMPIBAIJ.html">MATMPIBAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html">MKL Cluster PARDISO</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATDENSE.html">MATDENSE</a></span></code></p></td>
<td><p><a class="reference external" href="https://github.com/elemental/Elemental">Elemental</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Direct Cholesky</p></td>
<td><p>Cholesky</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCCHOLESKY.html">PCCHOLESKY</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQSBAIJ.html">MATSEQSBAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="http://pastix.gforge.inria.fr/files/README-txt.html">PaStiX</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSBAIJ.html">MATSBAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATDENSE.html">MATDENSE</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATNEST.html">MATNEST</a></span></code></p></td>
<td><p><a class="reference external" href="https://mumps-solver.org/">MUMPS</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQSBAIJ.html">MATSEQSBAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://people.engr.tamu.edu/davis/suitesparse.html">CHOLMOD (SuiteSparse)</a></p></td>
<td></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATDENSE.html">MATDENSE</a></span></code></p></td>
<td><p><a class="reference external" href="https://github.com/elemental/Elemental">Elemental</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQSBAIJ.html">MATSEQSBAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html">MKL PARDISO</a></p></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATMPIAIJ.html">MATMPIAIJ</a></span></code>, <code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATMPIBAIJ.html">MATMPIBAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://software.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top.html">MKL CPardiso</a></p></td>
<td><p>X</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>Direct SVD</p></td>
<td><p>Singular value decomposition</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCSVD.html">PCSVD</a></span></code></p></td>
<td><p>Any</p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Direct QR</p></td>
<td><p>QR</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/PC/PCQR.html">PCQR</a></span></code></p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATSEQAIJ.html">MATSEQAIJ</a></span></code></p></td>
<td><p><a class="reference external" href="https://people.engr.tamu.edu/davis/suitesparse.html">SuiteSparse QR</a></p></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td></td>
<td><p>XXt and XYt</p></td>
<td></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/Mat/MATAIJ.html">MATAIJ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td></td>
</tr>
</tbody>
</table>
</section>
<hr class="docutils" />
<section id="krylov-methods">
<h2>Krylov Methods<a class="headerlink" href="#krylov-methods" title="Link to this heading">#</a></h2>
<table class="table table-center">
<thead>
<tr class="row-odd"><th class="head"><p>Algorithm</p></th>
<th class="head"><p>Associated Type</p></th>
<th class="head"><p>External Packages</p></th>
<th class="head"><p>Parallel</p></th>
<th class="head"><p>Complex</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>Richardson</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPRICHARDSON.html">KSPRICHARDSON</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Chebyshev</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPCHEBYSHEV.html">KSPCHEBYSHEV</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>GMRES</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPGMRES.html">KSPGMRES</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Flexible GMRES</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPFGMRES.html">KSPFGMRES</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>LGMRES</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPLGMRES.html">KSPLGMRES</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Deflated GMRES</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPDGMRES.html">KSPDGMRES</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>Two-stage with least squares residual minimization</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPTSIRM.html">KSPTSIRM</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPCG.html">KSPCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Conjugate Gradient Squared</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPCGS.html">KSPCGS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Conjugate Gradient for Least Squares</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPCGLS.html">KSPCGLS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Conjugate Gradient on Normal Equations</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPCGNE.html">KSPCGNE</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Nash Conjugate Gradient with trust region constraint</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPNASH.html">KSPNASH</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Conjugate Gradient with trust region constraint</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPSTCG.html">KSPSTCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Gould et al Conjugate Gradient with trust region constraint</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPGLTR.html">KSPGLTR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Steinhaug Conjugate Gradient with trust region constraint</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPQCG.html">KSPQCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Left Conjugate Direction</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPLCD.html">KSPLCD</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Bi-Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPBICG.html">KSPBICG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Stabilized Bi-Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPBCGS.html">KSPBCGS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Improved Stabilized Bi-Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPIBCGS.html">KSPIBCGS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Transpose-free QMR</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPTFQMR.html">KSPTFQMR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Transpose-free variant of QMR developed by Tony Chan</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPTCQMR.html">KSPTCQMR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>QMR BiCGStab</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPQMRCGS.html">KSPQMRCGS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Flexible Conjugate Gradients</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPFCG.html">KSPFCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Flexible stabilized Bi-Conjugate Gradients</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPFBCGS.html">KSPFBCGS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Flexible stabilized Bi-Conjugate Gradients with fewer reductions</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPFBCGSR.html">KSPFBCGSR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Stabilized Bi-Conjugate Gradients with length <span class="math">\(\ell\)</span> recurrence</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPBCGSL.html">KSPBCGSL</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Conjugate Residual</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPCR.html">KSPCR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Generalized Conjugate Residual</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPGCR.html">KSPGCR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Generalized Conjugate Residual (with inner normalization and deflated restarts)</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPHPDDM.html">KSPHPDDM</a></span></code></p></td>
<td><p><a class="reference external" href="https://github.com/hpddm/hpddm">HPDDM</a></p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Minimum Residual</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPMINRES.html">KSPMINRES</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>LSQR</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPLSQR.html">KSPLSQR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>SYMMLQ</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPSYMMLQ.html">KSPSYMMLQ</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>FETI-DP (reduction to dual-primal sub-problem)</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPFETIDP.html">KSPFETIDP</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Gropp’s overlapped reduction pipelined Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPGROPPCG.html">KSPGROPPCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Pipelined Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPECG.html">KSPPIPECG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Pipelined Conjugate Gradient with residual replacement</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPECGRR.html">KSPPIPECGRR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Pipelined depth <span class="math">\(\ell\)</span> Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPELCG.html">KSPPIPELCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Pipelined predict-and-recompute Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPEPRCG.html">KSPPIPEPRCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Pipelined Conjugate Gradient over iteration pairs</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPECG2.html">KSPPIPECG2</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Pipelined flexible Conjugate Gradient</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPEFCG.html">KSPPIPEFCG</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Pipelined stabilized Bi-Conjugate Gradients</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPEBCGS.html">KSPPIPEBCGS</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Pipelined Conjugate Residual</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPECR.html">KSPPIPECR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Pipelined flexible GMRES</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPEFGMRES.html">KSPPIPEFGMRES</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-odd"><td><p>Pipelined Generalized Conjugate Residual</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPIPEGCR.html">KSPPIPEGCR</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
<tr class="row-even"><td><p>Pipelined GMRES</p></td>
<td><p><code class="docutils notranslate"><span class="pre"><a href="../manualpages/KSP/KSPPGMRES.html">KSPPGMRES</a></span></code></p></td>
<td><p>—</p></td>
<td><p>X</p></td>
<td><p>X</p></td>
</tr>
</tbody>
</table>
</section>
</section>
</article>
<footer class="prev-next-footer">
<div class="prev-next-area">
<a class="left-prev"
href="matrix_table.html"
title="previous page">
<i class="fa-solid fa-angle-left"></i>
<div class="prev-next-info">
<p class="prev-next-subtitle">previous</p>
<p class="prev-next-title">Summary of Matrix Types Available In PETSc</p>
</div>
</a>
<a class="right-next"
href="nonlinear_solve_table.html"
title="next page">
<div class="prev-next-info">
<p class="prev-next-subtitle">next</p>
<p class="prev-next-title">Summary of Nonlinear Solvers Available In PETSc</p>
</div>
<i class="fa-solid fa-angle-right"></i>
</a>
</div>
</footer>
</div>
<div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
<div class="sidebar-secondary-item">
<div
id="pst-page-navigation-heading-2"
class="page-toc tocsection onthispage">
<i class="fa-solid fa-list"></i> On this page
</div>
<nav class="bd-toc-nav page-toc" aria-labelledby="pst-page-navigation-heading-2">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#preconditioners">Preconditioners</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#direct-solvers">Direct Solvers</a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#krylov-methods">Krylov Methods</a></li>
</ul>
</nav></div>
<div class="sidebar-secondary-item">
<div class="tocsection editthispage">
<a href="https://gitlab.com/petsc/petsc/-/edit/release/doc/overview/linear_solve_table.md">
<i class="fa-solid fa-pencil"></i>
Edit on GitLab
</a>
</div>
</div>
<div class="sidebar-secondary-item">
<div class="tocsection sourcelink">
<a href="../_sources/overview/linear_solve_table.md.txt">
<i class="fa-solid fa-file-lines"></i> Show Source
</a>
</div>
</div>
</div></div>
</div>
<footer class="bd-footer-content">
</footer>
</main>
</div>
</div>
<!-- Scripts loaded after <body> so the DOM is not blocked -->
<script src="../_static/scripts/bootstrap.js?digest=bd9e20870c6007c4c509"></script>
<script src="../_static/scripts/pydata-sphinx-theme.js?digest=bd9e20870c6007c4c509"></script>
<footer class="bd-footer">
<div class="bd-footer__inner bd-page-width">
<div class="footer-items__start">
<div class="footer-item">
<p class="copyright">
© Copyright 1991-2025, UChicago Argonne, LLC and the PETSc Development Team.
<br/>
</p>
</div>
<div class="footer-item">
<p class="sphinx-version">
Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.3.7.
<br/>
</p>
</div>
</div>
<div class="footer-items__end">
<div class="footer-item">
<p class="theme-version">
Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.15.1.
</p></div>
<div class="footer-item"><p class="last-updated">
Last updated on 2025-04-30T13:10:40-0500 (v3.23.1).
<br/>
</p></div>
</div>
</div>
</footer>
</body>
</html>
|
