File: Linear-Algebra-References-and-Further-Reading.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 (137 lines) | stat: -rw-r--r-- 6,242 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
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
<!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: Linear Algebra References and Further Reading</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Linear Algebra References and Further Reading">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Linear Algebra References and Further Reading">
<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="Linear-Algebra.html#Linear-Algebra" rel="up" title="Linear Algebra">
<link href="Eigensystems.html#Eigensystems" rel="next" title="Eigensystems">
<link href="Linear-Algebra-Examples.html#Linear-Algebra-Examples" rel="previous" title="Linear Algebra Examples">
<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="Linear-Algebra-References-and-Further-Reading"></a>
<div class="header">
<p>
Previous: <a href="Linear-Algebra-Examples.html#Linear-Algebra-Examples" accesskey="p" rel="previous">Linear Algebra Examples</a>, Up: <a href="Linear-Algebra.html#Linear-Algebra" accesskey="u" rel="up">Linear Algebra</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="References-and-Further-Reading-8"></a>
<h3 class="section">14.21 References and Further Reading</h3>

<p>Further information on the algorithms described in this section can be
found in the following book,
</p>
<ul class="no-bullet">
<li><!-- /@w --> G. H. Golub, C. F. Van Loan, <cite>Matrix Computations</cite> (3rd Ed, 1996),
Johns Hopkins University Press, ISBN 0-8018-5414-8.
</li></ul>

<p>The <small>LAPACK</small> library is described in the following manual,
</p>
<ul class="no-bullet">
<li><!-- /@w --> <cite>LAPACK Users&rsquo; Guide</cite> (Third Edition, 1999), Published by SIAM,
ISBN 0-89871-447-8.

<p><a href="http://www.netlib.org/lapack">http://www.netlib.org/lapack</a> 
</p></li></ul>

<p>The <small>LAPACK</small> source code can be found at the website above, along
with an online copy of the users guide.
</p>
<p>The Modified Golub-Reinsch algorithm is described in the following paper,
</p>
<ul class="no-bullet">
<li><!-- /@w --> T.F. Chan, &ldquo;An Improved Algorithm for Computing the Singular Value
Decomposition&rdquo;, <cite>ACM Transactions on Mathematical Software</cite>, 8
(1982), pp 72&ndash;83.
</li></ul>

<p>The Jacobi algorithm for singular value decomposition is described in
the following papers,
</p>
<ul class="no-bullet">
<li><!-- /@w --> J.C. Nash, &ldquo;A one-sided transformation method for the singular value
decomposition and algebraic eigenproblem&rdquo;, <cite>Computer Journal</cite>,
Volume 18, Number 1 (1975), p 74&ndash;76

</li><li><!-- /@w --> J.C. Nash and S. Shlien &ldquo;Simple algorithms for the partial singular
value decomposition&rdquo;, <cite>Computer Journal</cite>, Volume 30 (1987), p
268&ndash;275.

</li><li><!-- /@w --> James Demmel, Kre&#353;imir Veseli&#263;, &ldquo;Jacobi&rsquo;s Method is more accurate than
QR&rdquo;, <cite>Lapack Working Note 15</cite> (LAWN-15), October 1989. Available
from netlib, <a href="http://www.netlib.org/lapack/">http://www.netlib.org/lapack/</a> in the <code>lawns</code> or
<code>lawnspdf</code> directories.
</li></ul>

<p>The algorithm for estimating a matrix condition number is described in
the following paper,
</p>
<ul class="no-bullet">
<li><!-- /@w --> N. J. Higham, &quot;FORTRAN codes for estimating the one-norm of
a real or complex matrix, with applications to condition estimation&quot;,
ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
</li></ul>

<hr>
<div class="header">
<p>
Previous: <a href="Linear-Algebra-Examples.html#Linear-Algebra-Examples" accesskey="p" rel="previous">Linear Algebra Examples</a>, Up: <a href="Linear-Algebra.html#Linear-Algebra" accesskey="u" rel="up">Linear Algebra</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>



</body>
</html>