\documentclass[10pt]{article}
\usepackage{longtable}

\begin{document}

\appendix

\section{Comprehensive Computational Results} \label{s:ResultsALL}

Tables \ref{supptab:all_large}, \ref{supptab:all_medium}, and \ref{supptab:all_small} present exhaustive computational results for large (those requiring $\geq1$ minute of run time), medium (those requiring between 1 minute and 0.1 seconds of run time), and small (those requiring $< 0.1$ seconds of run time) instances, respectively. In each table, the first three columns give the name (or index from SJ database), dimension, and number of nonzeros in each matrix. Column 4 gives the run time of the selected pivoting scheme tol 0. Lastly, columns 5, 6, 7, and 8 give the relative run time of small, large, diag, and tol 0.1 pivoting, respectively. \newpage

\begin{longtable}{|l|r|r|r|r|r|r|r|}
\hline	
& & & & \multicolumn{4}{c|}{Relative Run Time}  \\ \hline
\multicolumn{1}{|c|}{Matrix Name}	& \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{tol 0 run time (s)} & \multicolumn{1}{c|}{small} & \multicolumn{1}{c|}{large} & \multicolumn{1}{c|}{diag} & \multicolumn{1}{c|}{tol 0.1} \\  \hline \endhead
350	&	6774	&	33744	&	37446.9	&	0.96	&	2.00	&	2.25	&	0.84	\\
367	&	7337	&	156508	&	36428.4	&	1.01	&	1.66	&	1.01	&	1.00	\\
696	&	14454	&	147972	&	35205.6	&	0.99	&	2.45	&	1.08	&	1.00	\\
695	&	14454	&	147972	&	34811.8	&	1.00	&	2.48	&	1.11	&	1.01	\\
213	&	3402	&	130371	&	29913.4	&	1.00	&	2.09	&	0.14	&	1.04	\\
352	&	5773	&	71701	&	29133.3	&	1.00	&	2.64	&	1.58	&	1.11	\\
119	&	3251	&	65875	&	27139.8	&	1.00	&	3.18	&	1.57	&	0.96	\\
344	&	3363	&	99471	&	26520.3	&	1.00	&	3.05	&	1.76	&	0.95	\\
337	&	5321	&	65693	&	24280.1	&	1.01	&	3.56	&	1.10	&	0.48	\\
117	&	3973	&	79077	&	23425.2	&	1.00	&	2.69	&	1.64	&	1.00	\\
346	&	7055	&	30082	&	22870.2	&	0.99	&	1.03	&	1.02	&	1.12	\\
347	&	7055	&	30082	&	21941.5	&	1.00	&	1.02	&	1.01	&	1.18	\\
140	&	3937	&	25407	&	18202.5	&	1.00	&	1.75	&	1.39	&	1.01	\\
221	&	4257	&	37465	&	16199.7	&	0.93	&	1.47	&	1.46	&	0.98	\\
222	&	4257	&	37465	&	16172.9	&	0.94	&	1.46	&	1.46	&	0.98	\\
223	&	4257	&	37465	&	16169.0	&	0.93	&	1.46	&	1.47	&	0.98	\\
142	&	3937	&	25407	&	15886.7	&	0.98	&	1.98	&	1.37	&	0.99	\\
341	&	2880	&	18229	&	15287.3	&	1.00	&	2.91	&	1.58	&	0.81	\\
349	&	4101	&	82682	&	12733.3	&	1.00	&	1.77	&	1.04	&	0.99	\\
pilot87.pre	&	1540	&	30916	&	9707.8	&	1.00	&	5.38	&	1.56	&	1.00	\\
118	&	2568	&	75628	&	7847.5	&	1.00	&	2.28	&	1.31	&	0.86	\\
pilot87	&	1625	&	31396	&	6666.3	&	1.00	&	5.05	&	1.56	&	0.99	\\
gen4	&	375	&	8919	&	4487.8	&	1.00	&	2.39	&	1.51	&	1.00	\\
217	&	4720	&	20042	&	4169.6	&	1.00	&	2.79	&	2.75	&	1.00	\\
self	&	924	&	157411	&	4157.9	&	1.00	&	1.38	&	0.77	&	1.00	\\
gen4.pre	&	367	&	9322	&	4043.2	&	1.01	&	2.55	&	1.40	&	1.00	\\
slptsk	&	2315	&	34430	&	3290.8	&	1.00	&	1.62	&	1.29	&	1.00	\\
gen1	&	329	&	11016	&	2665.3	&	1.00	&	4.63	&	1.85	&	1.00	\\
207	&	1919	&	32399	&	2029.3	&	1.00	&	1.90	&	1.35	&	1.00	\\
335	&	6747	&	29195	&	1973.1	&	1.00	&	0.58	&	1.00	&	1.00	\\
87	&	2500	&	12349	&	1611.3	&	1.02	&	2.49	&	2.31	&	1.18	\\
pla8\_sig185	&	39835	&	196256	&	1030.4	&	1.33	&	6.94	&	0.94	&	1.09	\\
355	&	1409	&	42760	&	834.0	&	1.00	&	1.65	&	1.60	&	1.00	\\
159	&	1050	&	26198	&	742.0	&	0.99	&	0.71	&	0.59	&	1.06	\\
pilot	&	1132	&	16624	&	602.3	&	1.00	&	5.39	&	1.34	&	1.00	\\
maros-r7	&	1350	&	31923	&	517.1	&	1.01	&	0.11	&	1.47	&	1.00	\\
320	&	1733	&	22189	&	498.2	&	1.00	&	1.25	&	1.08	&	1.01	\\
stat96v4	&	3139	&	23752	&	388.3	&	1.00	&	1.41	&	1.51	&	1.00	\\
pla85900.nov21	&	40304	&	230558	&	370.5	&	1.12	&	5.74	&	0.96	&	1.04	\\
153	&	765	&	24382	&	340.9	&	1.00	&	1.18	&	1.16	&	1.00	\\
58	&	3083	&	11767	&	337.0	&	1.00	&	1.08	&	1.03	&	1.00	\\
momentum3	&	3254	&	15159	&	321.7	&	1.00	&	5.58	&	1.00	&	1.00	\\
jendrec1	&	1779	&	34196	&	247.2	&	1.00	&	1.61	&	1.10	&	1.00	\\
296	&	1258	&	7682	&	239.7	&	1.00	&	1.44	&	1.01	&	1.00	\\
brd14051	&	16360	&	180847	&	184.4	&	0.94	&	19.37	&	1.05	&	1.01	\\
fome13	&	24884	&	70839	&	184.1	&	0.95	&	15.03	&	1.23	&	1.05	\\
240	&	1000	&	1000000	&	161.3	&	1.00	&	1.06	&	0.96	&	1.00	\\
236	&	1000	&	1000000	&	143.1	&	1.00	&	1.10	&	1.00	&	1.00	\\
mod2.pre	&	4422	&	12914	&	137.7	&	1.00	&	2.19	&	1.13	&	1.00	\\
260	&	1000	&	1000000	&	134.1	&	0.99	&	1.07	&	1.03	&	0.99	\\
world	&	4261	&	12190	&	130.5	&	1.05	&	2.64	&	1.17	&	1.00	\\
l30	&	2492	&	12653	&	128.8	&	1.00	&	2.16	&	1.00	&	1.05	\\
340	&	8765	&	42471	&	109.4	&	0.99	&	0.89	&	0.88	&	0.99	\\
cont11\_l	&	58936	&	179556	&	108.3	&	0.98	&	0.84	&	0.98	&	0.97	\\
mod2	&	4435	&	12985	&	104.4	&	1.00	&	2.52	&	1.11	&	0.99	\\
309	&	2837	&	10967	&	95.1	&	1.00	&	1.22	&	0.99	&	1.00	\\
314	&	2836	&	10965	&	94.6	&	1.00	&	1.23	&	1.00	&	1.01	\\
232	&	1000	&	1000000	&	86.2	&	1.01	&	1.70	&	1.60	&	1.10	\\
gen2	&	328	&	8894	&	81.2	&	1.00	&	1.70	&	1.59	&	1.00	\\
scfxm1-2r-256	&	11812	&	44985	&	66.8	&	1.01	&	1.21	&	1.03	&	0.99	\\
\hline
\caption{Comprehensive Results: Large Instances}
\small
\centering
\label{supptab:all_large}
\end{longtable}

\begin{longtable}{|l|r|r|r|r|r|r|r|}
\hline	
& & & & \multicolumn{4}{c|}{Relative Run Time}  \\ \hline
\multicolumn{1}{|c|}{Matrix Name}	& \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{tol 0 run time (s)} & \multicolumn{1}{c|}{small} & \multicolumn{1}{c|}{large} & \multicolumn{1}{c|}{diag} & \multicolumn{1}{c|}{tol 0.1} \\  \hline \endhead
nemswrld	&	2205	&	13323	&	53.50	&	1.02	&	2.20	&	1.02	&	1.00	\\
cont4	&	2802	&	11862	&	44.81	&	1.00	&	1.79	&	1.07	&	1.00	\\
rat5	&	902	&	12026	&	40.77	&	1.00	&	2.50	&	1.32	&	0.99	\\
nug30	&	14681	&	45627	&	37.07	&	0.94	&	58.78	&	1.88	&	1.31	\\
nug20	&	7733	&	31455	&	35.20	&	0.98	&	53.50	&	4.31	&	1.35	\\
stat96v1	&	5013	&	20325	&	34.16	&	1.18	&	67.21	&	0.98	&	1.00	\\
stat96v2	&	12928	&	48009	&	32.85	&	0.91	&	9.45	&	0.94	&	1.01	\\
210	&	1484	&	6110	&	29.97	&	1.01	&	0.85	&	0.92	&	1.00	\\
pla33810	&	18940	&	123445	&	29.57	&	0.85	&	5.37	&	1.08	&	0.85	\\
stat96v3	&	13485	&	49917	&	27.62	&	0.94	&	7.57	&	1.04	&	1.01	\\
nug15	&	5486	&	24736	&	26.99	&	0.87	&	28.01	&	3.25	&	1.23	\\
pilot.ja	&	567	&	3781	&	25.13	&	1.00	&	5.37	&	2.78	&	1.00	\\
model10	&	1341	&	6403	&	24.62	&	1.01	&	3.02	&	1.05	&	1.00	\\
rat7a	&	641	&	10542	&	18.88	&	1.00	&	1.78	&	1.56	&	1.00	\\
d2q06c	&	1047	&	5717	&	18.27	&	1.00	&	1.15	&	1.49	&	0.99	\\
128	&	760	&	5739	&	18.26	&	1.00	&	0.94	&	0.74	&	0.92	\\
d15112	&	9197	&	47335	&	17.95	&	1.00	&	11.58	&	1.01	&	1.00	\\
141	&	511	&	2796	&	16.60	&	1.00	&	1.81	&	1.45	&	1.00	\\
144	&	511	&	2796	&	16.49	&	0.99	&	1.57	&	1.56	&	0.98	\\
progas	&	1167	&	6500	&	14.19	&	1.00	&	2.80	&	1.05	&	1.00	\\
co9	&	2287	&	13481	&	13.06	&	1.00	&	5.77	&	1.15	&	1.00	\\
stat96v5	&	812	&	3795	&	13.00	&	1.06	&	1.12	&	1.02	&	1.00	\\
l30.pre	&	1199	&	6030	&	12.56	&	1.00	&	2.32	&	1.02	&	0.99	\\
scfxm1-2b-64	&	5966	&	22682	&	12.11	&	1.00	&	1.22	&	1.04	&	0.99	\\
158	&	416	&	8562	&	12.08	&	0.99	&	1.97	&	1.03	&	0.99	\\
scfxm1-2r-128	&	5671	&	21943	&	11.80	&	1.00	&	1.25	&	1.05	&	1.00	\\
332	&	4101	&	36879	&	11.67	&	1.00	&	1.32	&	1.26	&	1.00	\\
NSR8K	&	5387	&	46157	&	11.62	&	0.89	&	27.59	&	1.76	&	1.07	\\
qap12	&	2740	&	12014	&	10.96	&	1.10	&	6.11	&	1.41	&	1.11	\\
newman2	&	468	&	7917	&	10.85	&	1.00	&	8.93	&	1.18	&	1.00	\\
watson\_1	&	5729	&	14544	&	9.00	&	1.15	&	1.55	&	0.99	&	1.00	\\
209	&	415	&	2779	&	8.66	&	0.99	&	1.16	&	1.16	&	1.03	\\
pilotnov	&	549	&	3337	&	8.64	&	1.01	&	4.68	&	1.23	&	1.00	\\
239	&	500	&	250000	&	8.38	&	1.00	&	1.11	&	0.99	&	1.02	\\
momentum2	&	2113	&	6516	&	8.35	&	0.99	&	6.52	&	1.00	&	0.99	\\
238	&	200	&	40000	&	8.32	&	0.99	&	1.03	&	1.02	&	0.99	\\
pilot4	&	289	&	2805	&	7.75	&	1.00	&	1.81	&	1.47	&	1.01	\\
235	&	500	&	250000	&	7.52	&	1.00	&	1.11	&	1.00	&	1.01	\\
231	&	500	&	250000	&	7.43	&	1.29	&	1.08	&	1.02	&	0.94	\\
dbic1	&	4795	&	23403	&	7.18	&	0.98	&	24.42	&	1.09	&	1.09	\\
perold	&	440	&	2584	&	7.13	&	1.01	&	2.91	&	2.16	&	1.00	\\
259	&	500	&	250000	&	7.12	&	1.00	&	1.13	&	1.09	&	1.02	\\
watson\_1.pre	&	4642	&	12991	&	7.05	&	1.18	&	1.45	&	1.00	&	1.00	\\
cont1\_l	&	1070	&	4649	&	6.23	&	0.97	&	1.60	&	1.17	&	1.01	\\
scfxm1-2r-96	&	4504	&	17205	&	6.22	&	1.00	&	1.24	&	1.06	&	1.00	\\
126	&	1220	&	5884	&	5.99	&	1.00	&	0.87	&	1.34	&	1.03	\\
291	&	1220	&	5860	&	5.91	&	1.00	&	0.76	&	1.18	&	1.01	\\
212	&	882	&	3354	&	5.87	&	0.95	&	0.89	&	1.17	&	0.96	\\
125	&	1220	&	5892	&	5.69	&	0.97	&	0.69	&	1.18	&	0.92	\\
nug12	&	2736	&	12037	&	5.62	&	1.13	&	8.35	&	1.90	&	1.01	\\
288	&	1220	&	5852	&	5.55	&	1.00	&	0.77	&	1.14	&	1.03	\\
pcb3038	&	3588	&	46560	&	5.41	&	0.84	&	18.72	&	1.78	&	1.01	\\
127	&	1220	&	5855	&	5.39	&	1.04	&	0.77	&	1.36	&	0.97	\\
model11	&	2039	&	7606	&	5.28	&	1.01	&	1.44	&	1.02	&	1.00	\\
294	&	1220	&	5892	&	5.20	&	0.96	&	0.76	&	1.18	&	0.94	\\
287	&	1220	&	5888	&	4.65	&	0.98	&	0.80	&	1.10	&	0.97	\\
289	&	1220	&	5884	&	4.39	&	0.98	&	0.69	&	1.07	&	0.93	\\
292	&	1220	&	5888	&	4.29	&	1.04	&	0.83	&	1.15	&	1.02	\\
nemspmm2	&	949	&	6478	&	4.24	&	1.09	&	3.08	&	1.15	&	1.02	\\
211	&	768	&	2934	&	4.01	&	1.00	&	0.94	&	1.05	&	0.97	\\
293	&	1220	&	5892	&	3.40	&	0.99	&	0.76	&	1.10	&	1.05	\\
stormg2\_1000.pre	&	13926	&	32547	&	3.27	&	2.10	&	1.29	&	1.01	&	1.00	\\
124	&	1220	&	5892	&	2.91	&	1.02	&	0.99	&	1.24	&	0.87	\\
stormg2\_1000	&	14075	&	32597	&	2.90	&	1.84	&	1.32	&	1.00	&	1.01	\\
152	&	180	&	2659	&	2.60	&	1.02	&	0.98	&	0.71	&	0.92	\\
fome12	&	12652	&	35969	&	2.53	&	0.99	&	9.31	&	1.36	&	1.09	\\
nl	&	890	&	2919	&	2.46	&	1.02	&	2.97	&	1.61	&	1.03	\\
fnl4461	&	5044	&	46977	&	2.36	&	1.10	&	13.36	&	1.22	&	1.15	\\
model6	&	790	&	3425	&	2.35	&	0.99	&	2.00	&	1.01	&	0.97	\\
scfxm1-2r-64	&	1870	&	11122	&	2.31	&	1.02	&	1.25	&	1.02	&	1.01	\\
co5	&	928	&	6173	&	2.26	&	1.01	&	8.86	&	1.16	&	1.00	\\
pla7397	&	5059	&	42683	&	2.17	&	0.90	&	9.43	&	0.99	&	1.06	\\
nemspmm1	&	982	&	5023	&	2.12	&	1.10	&	1.68	&	1.15	&	1.01	\\
315	&	2053	&	18447	&	2.09	&	0.98	&	1.31	&	1.25	&	0.98	\\
rl11849	&	6769	&	40885	&	2.09	&	1.02	&	7.09	&	0.82	&	0.88	\\
d18512	&	10815	&	55880	&	1.99	&	1.00	&	7.87	&	1.04	&	1.04	\\
cq9	&	1187	&	5786	&	1.52	&	1.03	&	4.54	&	1.14	&	1.03	\\
qap10	&	1510	&	6381	&	1.49	&	0.86	&	5.31	&	1.34	&	1.01	\\
de080285	&	368	&	1493	&	1.41	&	1.01	&	5.97	&	1.25	&	1.00	\\
rail4284	&	2463	&	11802	&	1.37	&	1.02	&	13.22	&	1.29	&	1.09	\\
pilot.we	&	554	&	2367	&	1.27	&	1.07	&	2.94	&	1.19	&	1.06	\\
newman	&	334	&	2156	&	1.24	&	0.97	&	4.24	&	0.93	&	0.95	\\
ge	&	1675	&	4758	&	1.14	&	1.03	&	2.63	&	1.03	&	1.03	\\
rat1	&	452	&	2893	&	1.10	&	1.00	&	0.73	&	0.98	&	1.00	\\
dano3mip.pre	&	1091	&	5239	&	1.08	&	1.04	&	10.64	&	1.42	&	0.95	\\
342	&	10001	&	49999	&	0.98	&	1.05	&	1.59	&	0.86	&	0.93	\\
t0331-4l	&	520	&	5034	&	0.91	&	1.00	&	2.50	&	1.46	&	1.09	\\
132	&	216	&	812	&	0.89	&	0.89	&	1.17	&	1.66	&	1.08	\\
model5	&	492	&	2247	&	0.88	&	0.99	&	2.15	&	1.09	&	1.03	\\
dano3mip	&	1135	&	5390	&	0.85	&	1.26	&	13.15	&	1.65	&	1.12	\\
grow22	&	434	&	4711	&	0.85	&	1.02	&	1.11	&	1.13	&	1.04	\\
rl5915	&	3853	&	28829	&	0.82	&	1.06	&	9.93	&	1.32	&	1.22	\\
model9	&	902	&	4361	&	0.75	&	1.09	&	1.89	&	1.06	&	1.09	\\
siena1	&	1265	&	11573	&	0.67	&	1.03	&	27.21	&	3.06	&	1.50	\\
fome11	&	6226	&	17749	&	0.64	&	1.00	&	13.28	&	1.37	&	1.17	\\
model7	&	646	&	2850	&	0.64	&	1.03	&	2.14	&	1.08	&	1.08	\\
rl5934	&	3773	&	23917	&	0.63	&	1.14	&	13.40	&	1.23	&	0.95	\\
nesm	&	279	&	895	&	0.63	&	1.10	&	2.29	&	1.24	&	1.01	\\
model4	&	409	&	1898	&	0.57	&	0.99	&	2.71	&	1.11	&	1.08	\\
de063155	&	313	&	1233	&	0.54	&	1.05	&	7.73	&	1.08	&	1.05	\\
lp22.pre	&	1811	&	13146	&	0.52	&	1.13	&	7.03	&	1.41	&	1.03	\\
orna1	&	810	&	2842	&	0.51	&	1.01	&	1.02	&	0.80	&	1.00	\\
lp22	&	1796	&	13076	&	0.49	&	1.16	&	7.18	&	1.43	&	1.29	\\
scfxm1-2r-32	&	1447	&	5658	&	0.46	&	1.09	&	1.16	&	1.06	&	1.00	\\
233	&	100	&	10000	&	0.44	&	1.00	&	0.88	&	0.89	&	0.89	\\
van	&	7417	&	21681	&	0.44	&	1.09	&	42.86	&	1.05	&	1.06	\\
usa13509	&	3595	&	19919	&	0.43	&	3.16	&	3.93	&	0.98	&	0.98	\\
237	&	100	&	10000	&	0.40	&	1.06	&	1.06	&	1.14	&	1.02	\\
arki001	&	160	&	893	&	0.37	&	1.00	&	2.16	&	1.09	&	1.02	\\
230	&	200	&	40000	&	0.37	&	0.95	&	1.06	&	0.98	&	0.94	\\
greenbeb	&	713	&	3278	&	0.36	&	1.15	&	1.83	&	1.03	&	1.15	\\
234	&	200	&	40000	&	0.35	&	1.00	&	1.06	&	0.95	&	0.97	\\
280	&	430	&	1544	&	0.35	&	1.01	&	0.96	&	0.75	&	0.84	\\
258	&	200	&	40000	&	0.35	&	0.99	&	0.99	&	1.01	&	0.93	\\
grow15	&	297	&	3614	&	0.34	&	1.00	&	0.84	&	1.06	&	0.98	\\
complex	&	327	&	10738	&	0.33	&	1.05	&	3.00	&	1.52	&	1.20	\\
scfxm1-2r-27	&	1222	&	4753	&	0.33	&	1.02	&	1.24	&	0.96	&	1.03	\\
newman3	&	369	&	3662	&	0.30	&	1.24	&	3.54	&	1.05	&	1.10	\\
momentum1	&	932	&	2792	&	0.30	&	0.94	&	5.16	&	0.85	&	0.75	\\
dfl001	&	3271	&	9276	&	0.27	&	1.22	&	13.44	&	1.89	&	1.14	\\
dfl001.pre	&	2097	&	6501	&	0.27	&	1.08	&	8.80	&	1.20	&	0.88	\\
stair	&	324	&	3431	&	0.27	&	0.94	&	1.85	&	1.64	&	1.02	\\
stocfor3	&	1782	&	4562	&	0.26	&	1.35	&	2.27	&	1.32	&	1.19	\\
large000	&	823	&	2282	&	0.25	&	1.05	&	1.03	&	1.02	&	1.04	\\
ulevimin	&	697	&	1879	&	0.24	&	1.11	&	3.35	&	0.97	&	0.91	\\
t1717	&	549	&	3657	&	0.24	&	1.06	&	4.23	&	1.90	&	1.45	\\
de063157	&	282	&	1102	&	0.24	&	1.33	&	6.22	&	0.75	&	1.27	\\
car4	&	122	&	4384	&	0.22	&	1.03	&	3.15	&	1.26	&	0.86	\\
greenbea	&	664	&	2706	&	0.21	&	0.99	&	1.46	&	0.98	&	1.18	\\
pcb3000	&	3058	&	27446	&	0.21	&	1.22	&	6.63	&	1.54	&	1.68	\\
25fv47	&	416	&	2061	&	0.21	&	0.86	&	1.05	&	0.96	&	0.94	\\
277	&	183	&	1069	&	0.20	&	1.20	&	9.67	&	8.55	&	1.50	\\
stp3d	&	10642	&	25936	&	0.20	&	2.85	&	7.97	&	1.09	&	0.88	\\
trento1	&	1070	&	10010	&	0.19	&	1.30	&	12.97	&	1.68	&	1.63	\\
cq5	&	570	&	2615	&	0.19	&	1.19	&	2.60	&	1.27	&	1.18	\\
dc1l	&	851	&	5171	&	0.18	&	1.17	&	7.53	&	1.70	&	1.13	\\
gran	&	284	&	1958	&	0.17	&	0.98	&	0.93	&	0.98	&	1.00	\\
dg012142	&	892	&	3627	&	0.15	&	1.12	&	1.57	&	1.03	&	1.02	\\
nug08	&	732	&	3004	&	0.15	&	1.00	&	4.48	&	1.43	&	1.19	\\
watson\_2	&	1011	&	2703	&	0.15	&	0.84	&	1.40	&	0.71	&	1.06	\\
dc1c	&	808	&	4698	&	0.14	&	1.12	&	8.40	&	1.79	&	1.25	\\
scfxm1-2r-16	&	752	&	2962	&	0.13	&	1.20	&	1.20	&	0.92	&	1.25	\\
air04	&	630	&	4187	&	0.12	&	0.79	&	2.80	&	1.68	&	1.27	\\
aa01	&	630	&	4187	&	0.12	&	0.76	&	3.38	&	1.41	&	1.48	\\
nemsemm2	&	789	&	2440	&	0.12	&	1.34	&	5.26	&	1.53	&	1.45	\\
scfxm1-2b-16	&	784	&	2975	&	0.12	&	1.08	&	0.98	&	1.06	&	0.99	\\
pf2177	&	406	&	1772	&	0.12	&	1.23	&	2.51	&	1.11	&	1.29	\\
dolom1	&	806	&	5681	&	0.11	&	1.29	&	4.28	&	1.25	&	0.99	\\
model3	&	310	&	1417	&	0.10	&	1.00	&	2.08	&	1.15	&	0.82	\\
\hline
\caption{Comprehensive Results: Medium Instances}
\small
\centering
\label{supptab:all_medium}
\end{longtable}

\begin{longtable}{|l|r|r|r|r|r|r|r|}
\hline	
& & & & \multicolumn{4}{c|}{Relative Run Time}  \\ \hline
\multicolumn{1}{|c|}{Matrix Name}	& \multicolumn{1}{c|}{n} & \multicolumn{1}{c|}{nnz} & \multicolumn{1}{c|}{tol 0 run time (s)} & \multicolumn{1}{c|}{small} & \multicolumn{1}{c|}{large} & \multicolumn{1}{c|}{diag} & \multicolumn{1}{c|}{tol 0.1} \\  \hline \endhead
ds	&	647	&	12193	&	0.0985	&	1.38	&	2.97	&	1.15	&	1.14	\\
ch	&	393	&	1304	&	0.0921	&	1.05	&	1.95	&	0.59	&	0.73	\\
nug07	&	450	&	1780	&	0.0892	&	0.96	&	1.94	&	0.69	&	0.88	\\
229	&	100	&	10000	&	0.0851	&	0.83	&	0.70	&	0.96	&	0.56	\\
cr42	&	304	&	608	&	0.0810	&	1.29	&	1.31	&	0.69	&	0.84	\\
143	&	131	&	536	&	0.0805	&	1.03	&	0.88	&	0.93	&	1.26	\\
delf000	&	593	&	1606	&	0.0723	&	1.55	&	1.11	&	0.53	&	1.03	\\
257	&	100	&	10000	&	0.0699	&	0.69	&	0.76	&	0.93	&	1.01	\\
air06	&	562	&	3420	&	0.0679	&	0.80	&	2.38	&	0.91	&	0.68	\\
protfold	&	574	&	2562	&	0.0671	&	0.96	&	4.55	&	1.32	&	1.04	\\
pldd000b	&	537	&	1448	&	0.0659	&	0.94	&	1.37	&	1.08	&	1.33	\\
279	&	261	&	2319	&	0.0646	&	1.24	&	1.46	&	1.44	&	0.62	\\
msc98-ip	&	2897	&	10006	&	0.0632	&	1.57	&	3.21	&	1.11	&	0.97	\\
l9	&	241	&	1381	&	0.0618	&	1.32	&	2.14	&	0.87	&	1.20	\\
model2	&	149	&	757	&	0.0616	&	1.06	&	1.35	&	1.10	&	0.53	\\
pcb1000	&	1156	&	9955	&	0.0615	&	1.00	&	4.20	&	2.54	&	1.40	\\
aa03	&	562	&	3420	&	0.0579	&	1.00	&	2.51	&	0.95	&	1.10	\\
lpl1	&	2692	&	7211	&	0.0516	&	0.93	&	2.25	&	0.64	&	0.65	\\
biella1	&	813	&	5726	&	0.0503	&	1.16	&	3.22	&	1.38	&	1.28	\\
grow7	&	138	&	1744	&	0.0491	&	1.09	&	1.20	&	0.96	&	1.61	\\
bg512142	&	560	&	2140	&	0.0471	&	1.06	&	1.52	&	0.77	&	0.81	\\
139	&	131	&	536	&	0.0453	&	1.06	&	1.90	&	2.00	&	2.23	\\
rosen10	&	989	&	6916	&	0.0423	&	1.48	&	0.82	&	1.75	&	0.92	\\
stormg2-125.pre	&	1780	&	4138	&	0.0404	&	0.91	&	1.02	&	0.94	&	0.92	\\
df2177	&	414	&	1825	&	0.0396	&	1.62	&	4.24	&	2.67	&	1.74	\\
stormg2-125	&	1886	&	4372	&	0.0394	&	0.97	&	1.04	&	1.08	&	0.92	\\
rosen2	&	431	&	4143	&	0.0363	&	1.16	&	1.02	&	0.82	&	0.44	\\
degen3	&	744	&	5431	&	0.0352	&	1.46	&	4.44	&	0.88	&	1.34	\\
10teams	&	177	&	885	&	0.0350	&	1.01	&	0.90	&	1.14	&	1.07	\\
scsd8	&	247	&	655	&	0.0344	&	0.47	&	0.93	&	0.76	&	0.60	\\
pds-80	&	9225	&	19432	&	0.0336	&	1.04	&	1.72	&	1.08	&	0.84	\\
bas1lp	&	502	&	6651	&	0.0328	&	0.82	&	4.64	&	1.09	&	0.60	\\
pilot4i	&	134	&	1220	&	0.0315	&	1.15	&	2.67	&	1.47	&	1.93	\\
cycle	&	284	&	878	&	0.0299	&	1.14	&	0.54	&	0.68	&	1.02	\\
pds-100	&	8377	&	17555	&	0.0297	&	1.09	&	2.22	&	0.67	&	0.77	\\
scfxm1-2r-8	&	403	&	1608	&	0.0294	&	1.08	&	1.56	&	1.19	&	1.68	\\
air05	&	323	&	1789	&	0.0287	&	1.02	&	1.92	&	0.96	&	0.88	\\
pds-60	&	7586	&	16067	&	0.0256	&	1.09	&	1.29	&	0.79	&	1.02	\\
gosh	&	379	&	1379	&	0.0249	&	1.33	&	1.60	&	1.22	&	0.59	\\
pds-90	&	7914	&	16673	&	0.0243	&	1.06	&	1.41	&	1.51	&	0.74	\\
pds-70	&	7822	&	16545	&	0.0214	&	2.02	&	2.67	&	0.86	&	1.58	\\
maros	&	289	&	1143	&	0.0213	&	1.09	&	1.27	&	1.31	&	0.54	\\
ganges	&	344	&	1123	&	0.0201	&	0.99	&	0.61	&	0.79	&	0.51	\\
fast0507	&	401	&	1908	&	0.0194	&	0.90	&	1.59	&	1.44	&	1.36	\\
bandm	&	122	&	609	&	0.0194	&	0.85	&	0.99	&	0.62	&	0.40	\\
pds-50	&	5962	&	12592	&	0.0187	&	1.24	&	2.14	&	1.47	&	1.42	\\
rail507	&	413	&	2005	&	0.0187	&	1.29	&	2.82	&	2.11	&	2.20	\\
30\_70\_4.5\_0.95\_100	&	2754	&	8381	&	0.0183	&	0.95	&	1.15	&	1.15	&	1.25	\\
baxter.pre	&	470	&	1274	&	0.0161	&	0.77	&	0.89	&	1.06	&	1.05	\\
modszk1	&	263	&	765	&	0.0159	&	0.85	&	3.40	&	0.95	&	1.99	\\
30\_70\_4.5\_0.95\_98	&	2451	&	7364	&	0.0154	&	1.18	&	1.31	&	1.12	&	1.17	\\
30\_70\_4.5\_0.5\_100	&	2098	&	6197	&	0.0148	&	0.63	&	1.02	&	0.73	&	0.82	\\
d6cube	&	223	&	1424	&	0.0147	&	2.61	&	8.60	&	3.46	&	2.95	\\
rentacar	&	327	&	1080	&	0.0141	&	1.24	&	0.75	&	1.16	&	1.42	\\
qiulp	&	603	&	1717	&	0.0138	&	1.97	&	2.90	&	1.24	&	1.83	\\
nug06	&	267	&	1007	&	0.0135	&	0.60	&	2.70	&	0.57	&	1.49	\\
qiu	&	603	&	1717	&	0.0133	&	1.89	&	3.43	&	1.24	&	1.78	\\
scfxm1-2c-4	&	233	&	965	&	0.0123	&	1.36	&	1.48	&	1.11	&	1.17	\\
rosen1	&	217	&	2528	&	0.0115	&	0.95	&	1.26	&	0.59	&	0.56	\\
pds-40	&	4028	&	8478	&	0.0110	&	1.52	&	0.68	&	1.49	&	1.49	\\
bnl2	&	459	&	1488	&	0.0107	&	1.19	&	1.71	&	0.87	&	1.33	\\
mitre	&	801	&	2466	&	0.0107	&	1.82	&	2.91	&	2.27	&	1.12	\\
pds-30	&	2643	&	5641	&	0.0107	&	0.96	&	1.24	&	1.08	&	0.87	\\
rail516	&	268	&	936	&	0.0098	&	0.96	&	1.91	&	0.99	&	0.74	\\
fome21	&	3291	&	7240	&	0.0098	&	1.25	&	2.72	&	2.10	&	1.87	\\
south31	&	112	&	460	&	0.0095	&	1.63	&	1.56	&	2.24	&	1.59	\\
rail582	&	384	&	1387	&	0.0093	&	0.95	&	1.82	&	1.39	&	1.59	\\
seymour	&	537	&	1881	&	0.0092	&	1.30	&	2.15	&	0.98	&	0.77	\\
scfxm1-2b-4	&	233	&	965	&	0.0084	&	1.38	&	1.73	&	1.18	&	0.95	\\
sp97ar	&	271	&	2400	&	0.0082	&	0.97	&	1.14	&	0.67	&	1.21	\\
neos6	&	174	&	1580	&	0.0082	&	0.95	&	2.29	&	0.75	&	0.93	\\
neos	&	2342	&	5098	&	0.0077	&	0.44	&	0.98	&	0.69	&	0.72	\\
r05	&	919	&	2717	&	0.0075	&	1.86	&	2.94	&	17.61	&	2.68	\\
manna81	&	1392	&	2784	&	0.0073	&	0.51	&	0.27	&	0.42	&	0.36	\\
p05	&	919	&	2717	&	0.0067	&	2.14	&	2.09	&	19.68	&	2.61	\\
scfxm1-2r-4	&	233	&	965	&	0.0065	&	1.21	&	1.07	&	1.62	&	2.07	\\
bnl1	&	223	&	824	&	0.0065	&	0.83	&	1.37	&	1.01	&	1.18	\\
rosen8	&	264	&	1850	&	0.0057	&	0.96	&	0.78	&	2.79	&	1.05	\\
scagr7-2r-864	&	680	&	1697	&	0.0057	&	1.44	&	1.35	&	1.09	&	1.73	\\
sp98ar	&	223	&	1782	&	0.0055	&	0.87	&	1.55	&	1.41	&	0.47	\\
fome20	&	1718	&	3811	&	0.0055	&	1.35	&	4.06	&	1.46	&	1.29	\\
scrs8-2r-512	&	992	&	1984	&	0.0054	&	0.43	&	0.76	&	0.68	&	0.90	\\
disctom	&	192	&	565	&	0.0052	&	0.79	&	2.07	&	1.75	&	1.66	\\
scfxm3	&	262	&	1005	&	0.0052	&	0.80	&	2.42	&	0.96	&	1.47	\\
danoint	&	196	&	790	&	0.0051	&	2.31	&	2.60	&	1.64	&	2.22	\\
mzzv11	&	1098	&	3189	&	0.0047	&	1.78	&	1.71	&	1.92	&	0.99	\\
80bau3b	&	154	&	396	&	0.0046	&	0.82	&	0.63	&	0.76	&	0.73	\\
dbir2.pre	&	281	&	1879	&	0.0043	&	1.10	&	0.93	&	1.14	&	1.70	\\
capri	&	138	&	507	&	0.0043	&	2.31	&	5.90	&	2.71	&	2.01	\\
p010	&	839	&	2486	&	0.0041	&	1.46	&	4.40	&	1.50	&	1.95	\\
degen2	&	217	&	1138	&	0.0040	&	1.68	&	0.96	&	0.99	&	0.79	\\
scfxm2	&	178	&	658	&	0.0037	&	1.22	&	1.08	&	1.17	&	1.11	\\
baxter	&	256	&	697	&	0.0037	&	0.83	&	0.80	&	0.89	&	0.57	\\
dbir1	&	154	&	845	&	0.0035	&	1.52	&	0.87	&	2.61	&	1.92	\\
small000	&	140	&	383	&	0.0034	&	1.44	&	0.73	&	1.11	&	1.46	\\
stormg2-27	&	449	&	1019	&	0.0034	&	1.07	&	0.71	&	0.55	&	0.58	\\
roll3000	&	177	&	1101	&	0.0034	&	1.27	&	2.48	&	1.22	&	1.01	\\
woodw	&	168	&	589	&	0.0032	&	1.52	&	4.88	&	1.17	&	1.68	\\
route	&	339	&	1290	&	0.0032	&	1.21	&	5.23	&	1.32	&	0.97	\\
nsct1	&	120	&	595	&	0.0031	&	0.88	&	1.37	&	1.40	&	1.56	\\
neos.pre	&	2080	&	4578	&	0.0029	&	1.12	&	1.34	&	1.59	&	2.06	\\
mzzv42z	&	787	&	2124	&	0.0027	&	1.33	&	1.81	&	1.78	&	2.01	\\
crew1	&	127	&	861	&	0.0027	&	1.48	&	3.04	&	0.74	&	1.46	\\
neos7	&	590	&	1434	&	0.0026	&	2.13	&	2.94	&	2.51	&	0.96	\\
sgpf5y6	&	787	&	1870	&	0.0022	&	1.11	&	1.58	&	1.46	&	1.01	\\
neos1	&	309	&	944	&	0.0022	&	2.16	&	2.84	&	1.24	&	1.85	\\
neos11	&	365	&	1116	&	0.0022	&	3.00	&	3.12	&	1.68	&	2.90	\\
nsct2.pre	&	156	&	1140	&	0.0021	&	1.13	&	0.74	&	1.86	&	0.81	\\
stocfor2	&	224	&	576	&	0.0021	&	2.28	&	5.07	&	2.93	&	2.33	\\
scrs8-2r-256	&	416	&	832	&	0.0020	&	1.12	&	0.38	&	0.62	&	1.47	\\
neos4	&	454	&	944	&	0.0020	&	0.72	&	0.91	&	1.04	&	0.43	\\
blp-ar98	&	148	&	876	&	0.0019	&	1.04	&	1.79	&	1.21	&	0.68	\\
dsbmip	&	220	&	568	&	0.0019	&	1.93	&	1.52	&	1.35	&	1.41	\\
sgpf5y6.pre	&	755	&	1744	&	0.0018	&	1.39	&	0.78	&	1.69	&	1.63	\\
neos823206	&	220	&	547	&	0.0015	&	0.57	&	1.58	&	1.04	&	0.95	\\
sc205	&	184	&	487	&	0.0015	&	0.65	&	0.78	&	0.83	&	0.82	\\
rosen7	&	127	&	649	&	0.0014	&	0.91	&	1.39	&	0.84	&	0.87	\\
scrs8-2r-64	&	256	&	512	&	0.0014	&	0.79	&	0.98	&	0.80	&	1.43	\\
pp08aCUTS	&	131	&	332	&	0.0013	&	0.62	&	0.61	&	0.81	&	0.64	\\
scorpion	&	131	&	507	&	0.0013	&	0.69	&	1.54	&	1.06	&	1.17	\\
lpl3	&	212	&	461	&	0.0013	&	0.53	&	0.48	&	1.06	&	0.83	\\
p19	&	117	&	555	&	0.0012	&	2.29	&	1.25	&	1.66	&	2.15	\\
iiasa	&	113	&	262	&	0.0012	&	0.76	&	0.95	&	0.90	&	1.53	\\
pds-20.pre	&	370	&	851	&	0.0012	&	1.71	&	1.42	&	1.33	&	0.76	\\
rd-rplusc-21	&	148	&	454	&	0.0011	&	1.55	&	1.47	&	1.27	&	1.64	\\
neos19	&	228	&	487	&	0.0011	&	1.33	&	1.17	&	0.82	&	1.55	\\
gesa2\_o	&	102	&	214	&	0.0011	&	0.97	&	0.41	&	0.77	&	0.53	\\
boeing1	&	122	&	415	&	0.0011	&	1.57	&	1.69	&	0.92	&	0.94	\\
gesa3\_o	&	148	&	365	&	0.0010	&	1.22	&	0.77	&	1.09	&	0.61	\\
gesa3	&	134	&	336	&	0.0010	&	1.18	&	0.62	&	1.19	&	0.94	\\
UMTS	&	268	&	828	&	0.0010	&	1.37	&	26.97	&	1.28	&	1.51	\\
scrs8	&	109	&	280	&	0.0010	&	0.60	&	1.02	&	1.15	&	1.65	\\
scrs8-2r-128	&	192	&	384	&	0.0010	&	1.27	&	1.26	&	0.74	&	1.13	\\
scrs8-2c-64	&	168	&	336	&	0.0009	&	0.45	&	1.07	&	0.67	&	1.39	\\
ceria3d	&	130	&	647	&	0.0009	&	1.52	&	1.88	&	0.98	&	1.11	\\
stormg2-8	&	117	&	263	&	0.0009	&	0.68	&	1.13	&	0.64	&	1.15	\\
nsct2	&	107	&	544	&	0.0009	&	1.13	&	1.12	&	1.87	&	1.66	\\
mkc	&	106	&	250	&	0.0009	&	0.96	&	0.48	&	0.97	&	0.44	\\
scrs8-2r-32	&	128	&	256	&	0.0009	&	1.19	&	0.80	&	0.79	&	0.91	\\
dbir2	&	157	&	784	&	0.0009	&	1.58	&	3.07	&	1.81	&	2.19	\\
neos818918	&	265	&	678	&	0.0009	&	1.71	&	2.65	&	2.86	&	0.98	\\
mkc1	&	106	&	250	&	0.0008	&	0.93	&	1.31	&	0.96	&	1.30	\\
bienst1	&	102	&	253	&	0.0006	&	0.77	&	0.65	&	0.92	&	1.58	\\
nug05	&	107	&	362	&	0.0006	&	1.19	&	2.43	&	2.42	&	3.04	\\
dcmulti	&	120	&	303	&	0.0005	&	1.42	&	0.80	&	0.96	&	1.15	\\
\hline
\caption{Comprehensive Results: Small Instances}
\small
\centering
\label{supptab:all_small}
\end{longtable}

\end{document}

