File: Numerical-Integration.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 (135 lines) | stat: -rw-r--r-- 9,279 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
<!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: Numerical Integration</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Numerical Integration">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Numerical Integration">
<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="Numerical-Integration-Introduction.html#Numerical-Integration-Introduction" rel="next" title="Numerical Integration Introduction">
<link href="FFT-References-and-Further-Reading.html#FFT-References-and-Further-Reading" rel="previous" title="FFT 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="Numerical-Integration"></a>
<div class="header">
<p>
Next: <a href="Random-Number-Generation.html#Random-Number-Generation" accesskey="n" rel="next">Random Number Generation</a>, Previous: <a href="Fast-Fourier-Transforms.html#Fast-Fourier-Transforms" accesskey="p" rel="previous">Fast Fourier Transforms</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="Numerical-Integration-1"></a>
<h2 class="chapter">17 Numerical Integration</h2>
<a name="index-quadrature"></a>
<a name="index-numerical-integration-_0028quadrature_0029"></a>
<a name="index-integration_002c-numerical-_0028quadrature_0029"></a>
<a name="index-QUADPACK"></a>

<p>This chapter describes routines for performing numerical integration
(quadrature) of a function in one dimension.  There are routines for
adaptive and non-adaptive integration of general functions, with
specialised routines for specific cases.  These include integration over
infinite and semi-infinite ranges, singular integrals, including
logarithmic singularities, computation of Cauchy principal values and
oscillatory integrals.  The library reimplements the algorithms used in
<small>QUADPACK</small>, a numerical integration package written by Piessens,
de Doncker-Kapenga, Ueberhuber and Kahaner.  Fortran code for <small>QUADPACK</small> is
available on Netlib.  Also included are non-adaptive, fixed-order
Gauss-Legendre integration routines with high precision coefficients
by Pavel Holoborodko.
</p>
<p>The functions described in this chapter are declared in the header file
<samp>gsl_integration.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Numerical-Integration-Introduction.html#Numerical-Integration-Introduction" accesskey="1">Numerical Integration Introduction</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QNG-non_002dadaptive-Gauss_002dKronrod-integration.html#QNG-non_002dadaptive-Gauss_002dKronrod-integration" accesskey="2">QNG non-adaptive Gauss-Kronrod integration</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAG-adaptive-integration.html#QAG-adaptive-integration" accesskey="3">QAG adaptive integration</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAGS-adaptive-integration-with-singularities.html#QAGS-adaptive-integration-with-singularities" accesskey="4">QAGS adaptive integration with singularities</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAGP-adaptive-integration-with-known-singular-points.html#QAGP-adaptive-integration-with-known-singular-points" accesskey="5">QAGP adaptive integration with known singular points</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAGI-adaptive-integration-on-infinite-intervals.html#QAGI-adaptive-integration-on-infinite-intervals" accesskey="6">QAGI adaptive integration on infinite intervals</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAWC-adaptive-integration-for-Cauchy-principal-values.html#QAWC-adaptive-integration-for-Cauchy-principal-values" accesskey="7">QAWC adaptive integration for Cauchy principal values</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAWS-adaptive-integration-for-singular-functions.html#QAWS-adaptive-integration-for-singular-functions" accesskey="8">QAWS adaptive integration for singular functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAWO-adaptive-integration-for-oscillatory-functions.html#QAWO-adaptive-integration-for-oscillatory-functions" accesskey="9">QAWO adaptive integration for oscillatory functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="QAWF-adaptive-integration-for-Fourier-integrals.html#QAWF-adaptive-integration-for-Fourier-integrals">QAWF adaptive integration for Fourier integrals</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="CQUAD-doubly_002dadaptive-integration.html#CQUAD-doubly_002dadaptive-integration">CQUAD doubly-adaptive integration</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Fixed-order-Gauss_002dLegendre-integration.html#Fixed-order-Gauss_002dLegendre-integration">Fixed order Gauss-Legendre integration</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Numerical-integration-error-codes.html#Numerical-integration-error-codes">Numerical integration error codes</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Numerical-integration-examples.html#Numerical-integration-examples">Numerical integration examples</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Numerical-integration-References-and-Further-Reading.html#Numerical-integration-References-and-Further-Reading">Numerical integration References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<hr>
<div class="header">
<p>
Next: <a href="Random-Number-Generation.html#Random-Number-Generation" accesskey="n" rel="next">Random Number Generation</a>, Previous: <a href="Fast-Fourier-Transforms.html#Fast-Fourier-Transforms" accesskey="p" rel="previous">Fast Fourier Transforms</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>



</body>
</html>