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
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML3.2 EN">
<HTML>
<HEAD> <link rel="canonical" href="https://slepc.upv.es/documentation/current//Users/jroman/tmp/slepc-3.23.1/docs/manualpages/DS/DSPEP.html" />
<META NAME="GENERATOR" CONTENT="DOCTEXT">
<link rel="stylesheet" href="/slepc.css" type="text/css">
<TITLE>DSPEP</TITLE>
</HEAD>
<BODY BGCOLOR="FFFFFF">
<div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
<div id="bugreport" align=right><a href="mailto:slepc-maint@upv.es?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: slepc-3.23.1 v3.23.1 /Users/jroman/tmp/slepc-3.23.1/docs/manualpages/DS/DSPEP.html "><small>Report Typos and Errors</small></a></div>
<H1>DSPEP</H1>
Dense Polynomial Eigenvalue Problem.
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
The problem is expressed as P(lambda)*x = 0, where P(.) is a matrix
polynomial of degree d. The eigenvalues lambda are the arguments
returned by <A HREF="../DS/DSSolve.html#DSSolve">DSSolve</A>().
<P>
The degree of the polynomial, d, can be set with <A HREF="../DS/DSPEPSetDegree.html#DSPEPSetDegree">DSPEPSetDegree</A>(), with
the first d+1 extra matrices of the <A HREF="../DS/DS.html#DS">DS</A> defining the matrix polynomial. By
default, the polynomial is expressed in the monomial basis, but a
different basis can be used by setting the corresponding coefficients
via <A HREF="../DS/DSPEPSetCoefficients.html#DSPEPSetCoefficients">DSPEPSetCoefficients</A>().
<P>
The problem is solved via linearization, by building a pencil (A,B) of
size p*n and solving the corresponding GNHEP.
<P>
<H3><FONT COLOR="#883300">Used DS matrices</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>DS_MAT_Ex </B></TD><TD> - coefficients of the matrix polynomial
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_X</A> </B></TD><TD> - right eigenvectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_Y</A> </B></TD><TD> - left eigenvectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_A</A> </B></TD><TD> - (workspace) first matrix of the linearization
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_B</A> </B></TD><TD> - (workspace) second matrix of the linearization
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_W</A> </B></TD><TD> - (workspace) right eigenvectors of the linearization
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_U</A> </B></TD><TD> - (workspace) left eigenvectors of the linearization
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Implemented methods</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>0 </B></TD><TD> - QZ iteration on the linearization (_ggev)
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../DS/DSCreate.html#DSCreate">DSCreate</A>(), <A HREF="../DS/DSSetType.html#DSSetType">DSSetType</A>(), <A HREF="../DS/DSType.html#DSType">DSType</A>, <A HREF="../DS/DSPEPSetDegree.html#DSPEPSetDegree">DSPEPSetDegree</A>(), <A HREF="../DS/DSPEPSetCoefficients.html#DSPEPSetCoefficients">DSPEPSetCoefficients</A>()
<BR><P><B></B><H3><FONT COLOR="#883300">Level</FONT></H3>beginner<BR>
<H3><FONT COLOR="#883300">Location</FONT></H3>
</B><A HREF="../../../src/sys/classes/ds/impls/pep/dspep.c.html#DSPEP">src/sys/classes/ds/impls/pep/dspep.c</A>
<BR><BR><A HREF="./index.html">Index of all DS routines</A>
<BR><A HREF="../../../docs/manual.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
</BODY></HTML>
|
