File: Eigensystems.html

package info (click to toggle)
gsl-ref-html 2.3-1
  • links: PTS
  • area: non-free
  • in suites: bullseye, buster, sid
  • size: 6,876 kB
  • ctags: 4,574
  • sloc: makefile: 35
file content (111 lines) | stat: -rw-r--r-- 6,675 bytes parent folder | download
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
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled "GNU Free Documentation
License".

(a) The Back-Cover Text is: "You have the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library &ndash; Reference Manual: Eigensystems</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Eigensystems">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Eigensystems">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="index.html#Top" rel="up" title="Top">
<link href="Real-Symmetric-Matrices.html#Real-Symmetric-Matrices" rel="next" title="Real Symmetric Matrices">
<link href="Linear-Algebra-References-and-Further-Reading.html#Linear-Algebra-References-and-Further-Reading" rel="previous" title="Linear Algebra References and Further Reading">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Eigensystems"></a>
<div class="header">
<p>
Next: <a href="Fast-Fourier-Transforms.html#Fast-Fourier-Transforms" accesskey="n" rel="next">Fast Fourier Transforms</a>, Previous: <a href="Linear-Algebra.html#Linear-Algebra" accesskey="p" rel="previous">Linear Algebra</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Eigensystems-1"></a>
<h2 class="chapter">15 Eigensystems</h2>
<a name="index-eigenvalues-and-eigenvectors"></a>
<p>This chapter describes functions for computing eigenvalues and
eigenvectors of matrices.  There are routines for real symmetric,
real nonsymmetric, complex hermitian, real generalized symmetric-definite,
complex generalized hermitian-definite, and real generalized nonsymmetric
eigensystems. Eigenvalues can be computed with or without eigenvectors.
The hermitian and real symmetric matrix algorithms are symmetric bidiagonalization
followed by QR reduction. The nonsymmetric algorithm is the Francis QR
double-shift.  The generalized nonsymmetric algorithm is the QZ method due
to Moler and Stewart.
</p>
<p>The functions described in this chapter are declared in the header file
<samp>gsl_eigen.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Real-Symmetric-Matrices.html#Real-Symmetric-Matrices" accesskey="1">Real Symmetric Matrices</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Complex-Hermitian-Matrices.html#Complex-Hermitian-Matrices" accesskey="2">Complex Hermitian Matrices</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Real-Nonsymmetric-Matrices.html#Real-Nonsymmetric-Matrices" accesskey="3">Real Nonsymmetric Matrices</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Real-Generalized-Symmetric_002dDefinite-Eigensystems.html#Real-Generalized-Symmetric_002dDefinite-Eigensystems" accesskey="4">Real Generalized Symmetric-Definite Eigensystems</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Complex-Generalized-Hermitian_002dDefinite-Eigensystems.html#Complex-Generalized-Hermitian_002dDefinite-Eigensystems" accesskey="5">Complex Generalized Hermitian-Definite Eigensystems</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Real-Generalized-Nonsymmetric-Eigensystems.html#Real-Generalized-Nonsymmetric-Eigensystems" accesskey="6">Real Generalized Nonsymmetric Eigensystems</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Sorting-Eigenvalues-and-Eigenvectors.html#Sorting-Eigenvalues-and-Eigenvectors" accesskey="7">Sorting Eigenvalues and Eigenvectors</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Eigenvalue-and-Eigenvector-Examples.html#Eigenvalue-and-Eigenvector-Examples" accesskey="8">Eigenvalue and Eigenvector Examples</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Eigenvalue-and-Eigenvector-References.html#Eigenvalue-and-Eigenvector-References" accesskey="9">Eigenvalue and Eigenvector References</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>




</body>
</html>