File: Nonlinear-Least_002dSquares-TRS-2D-Subspace.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 (90 lines) | stat: -rw-r--r-- 4,933 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
<!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: Nonlinear Least-Squares TRS 2D Subspace</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Nonlinear Least-Squares TRS 2D Subspace">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Nonlinear Least-Squares TRS 2D Subspace">
<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="Nonlinear-Least_002dSquares-TRS-Overview.html#Nonlinear-Least_002dSquares-TRS-Overview" rel="up" title="Nonlinear Least-Squares TRS Overview">
<link href="Nonlinear-Least_002dSquares-TRS-Steihaug_002dToint-Conjugate-Gradient.html#Nonlinear-Least_002dSquares-TRS-Steihaug_002dToint-Conjugate-Gradient" rel="next" title="Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient">
<link href="Nonlinear-Least_002dSquares-TRS-Double-Dogleg.html#Nonlinear-Least_002dSquares-TRS-Double-Dogleg" rel="previous" title="Nonlinear Least-Squares TRS Double Dogleg">
<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="Nonlinear-Least_002dSquares-TRS-2D-Subspace"></a>
<div class="header">
<p>
Next: <a href="Nonlinear-Least_002dSquares-TRS-Steihaug_002dToint-Conjugate-Gradient.html#Nonlinear-Least_002dSquares-TRS-Steihaug_002dToint-Conjugate-Gradient" accesskey="n" rel="next">Nonlinear Least-Squares TRS Steihaug-Toint Conjugate Gradient</a>, Previous: <a href="Nonlinear-Least_002dSquares-TRS-Double-Dogleg.html#Nonlinear-Least_002dSquares-TRS-Double-Dogleg" accesskey="p" rel="previous">Nonlinear Least-Squares TRS Double Dogleg</a>, Up: <a href="Nonlinear-Least_002dSquares-TRS-Overview.html#Nonlinear-Least_002dSquares-TRS-Overview" accesskey="u" rel="up">Nonlinear Least-Squares TRS Overview</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Two-Dimensional-Subspace"></a>
<h4 class="subsection">39.2.5 Two Dimensional Subspace</h4>

<p>The dogleg methods restrict the search for the TRS solution
to a 1D curve defined by the Cauchy and Gauss-Newton points.
An improvement to this is to search for a solution using
the full two dimensional subspace spanned by the Cauchy
and Gauss-Newton directions. The dogleg path is of course
inside this subspace, and so this method solves the TRS
at least as accurately as the dogleg methods. Since this
method searches a larger subspace for a solution, it can
converge more quickly than dogleg on some problems. Because
the subspace is only two dimensional, this method is
very efficient and the main computation per iteration is
to determine the Gauss-Newton point.
</p>



</body>
</html>