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quadrule_fast.html
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<html>
<head>
<title>
QUADRULE_FAST - Efficient Quadrature Rule Implementation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
QUADRULE_FAST <br> Efficient Quadrature Rule Implementation
</h1>
<hr>
<p>
<b>QUADRULE_FAST</b>
is a MATLAB library which
implements fast and
efficient forms of several popular quadrature rules.
</p>
<p>
The quadrature rules are defined on the interval [-1,1], and
assume there is no additional weighting factor in the data.
</p>
<p>
The fast implementations are exhibited and discussed in
the papers by Trefethen and Waldvogel.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>QUADRULE_FAST</b> is available in
<a href = "../../m_src/quadrule_fast/quadrule_fast.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/clenshaw_curtis_rule/clenshaw_curtis_rule.html">
CLENSHAW_CURTIS_RULE</a>,
a MATLAB program which
can compute Clenshaw Curtis rules
for 1 dimensional or multidimensional problems.
</p>
<p>
<a href = "../../m_src/felippa/felippa.html">
FELIPPA</a>,
a MATLAB library which
defines quadrature rules for lines, triangles, quadrilaterals,
pyramids, wedges, tetrahedrons and hexahedrons.
</p>
<p>
<a href = "../../m_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a MATLAB program which
can create a multidimensional quadrature rule as a product of
one dimensional rules.
</p>
<p>
<a href = "../../f_src/quadpack/quadpack.html">
QUADPACK</a>,
a FORTRAN90 library which
contains a variety of routines for
numerical estimation of integrals in 1D.
</p>
<p>
<a href = "../../m_src/quadrature_test/quadrature_test.html">
QUADRATURE_TEST</a>,
a MATLAB program which
reads the definition of a
multidimensional quadrature rule from three files, applies
the rule to a number of test integrals, and prints the
results.
</p>
<p>
<a href = "../../m_src/quadrule/quadrule.html">
QUADRULE</a>,
a MATLAB library which
contains quadrature rules.
</p>
<p>
<a href = "../../m_src/stroud/stroud.html">
STROUD</a>,
a MATLAB library which
contains quadrature
rules for a variety of unusual areas, surfaces and volumes in 2D,
3D and N-dimensions.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
<li>
Charles Clenshaw, Alan Curtis,<br>
A Method for Numerical Integration on an Automatic Computer,<br>
Numerische Mathematik,<br>
Volume 2, Number 1, December 1960, pages 197-205.
</li>
<li>
Lloyd Trefethen,<br>
Is Gauss Quadrature Better Than Clenshaw-Curtis?,<br>
SIAM Review,<br>
Volume 50, Number 1, 2008, pages 67-87.
</li>
<li>
Joerg Waldvogel,<br>
Fast Construction of the Fejer and Clenshaw-Curtis Quadrature Rules,<br>
BIT Numerical Mathematics,<br>
Volume 43, Number 1, 2003, pages 1-18.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "clenshaw_curtis_integrate.m">
clenshaw_curtis_integrate.m</a>
applies a Clenshaw Curtis quadrature rule.
</li>
<li>
<a href = "clenshaw_curtis_integrate_fast.m">
clenshaw_curtis_integrate_fast.m</a>
applies a Clenshaw Curtis quadrature rule,
using an efficient MATLAB implementation.
</li>
<li>
<a href = "clenshaw_curtis_rule_compute.m">
clenshaw_curtis_rule_compute.m</a>
computes a Clenshaw Curtis quadrature rule.
</li>
<li>
<a href = "clenshaw_curtis_rule_set.m">clenshaw_curtis_rule_set.m</a>
sets a Clenshaw Curtis quadrature rule by looking it up in a table.
</li>
<li>
<a href = "fejer1_integrate_fast.m">
fejer1_integrate_fast.m</a>
applies a Fejer type 1 quadrature rule,
using an efficient MATLAB implementation.
</li>
<li>
<a href = "fejer1_rule_compute.m">
fejer1_rule_compute.m</a>
computes a Fejer type 1 quadrature rule.
</li>
<li>
<a href = "fejer1_rule_set.m">fejer1_rule_set.m</a>
sets a Fejer type 1 quadrature rule by looking it up in a table.
</li>
<li>
<a href = "fejer2_integrate_fast.m">
fejer2_integrate_fast.m</a>
applies a Fejer type 2 quadrature rule,
using an efficient MATLAB implementation.
</li>
<li>
<a href = "fejer2_rule_compute.m">
fejer2_rule_compute.m</a>
computes a Fejer type 2 quadrature rule.
</li>
<li>
<a href = "fejer2_rule_set.m">fejer2_rule_set.m</a>
sets a Fejer type 2 quadrature rule by looking it up in a table.
</li>
<li>
<a href = "gauss_legendre_integrate_fast.m">
gauss_legendre_integrate_fast.m</a>
applies a Gauss-Legendre quadrature rule,
using an efficient MATLAB implementation.
</li>
<li>
<a href = "gauss_legendre_rule_compute.m">
gauss_legendre_rule_compute.m</a>
computes a Gauss Legendre quadrature rule.
</li>
<li>
<a href = "gauss_legendre_rule_set.m">gauss_legendre_rule_set.m</a>
sets a Gauss Legendre quadrature rule by looking it up in a table.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "quadrule_fast_test.m">quadrule_fast_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "quadrule_fast_test.out">quadrule_fast_test.out</a>,
the output from a run of the sample program.
</li>
<li>
<a href = "quadrule_fast_test01.m">quadrule_fast_test01.m</a>,
compares CLENSHAW_CURTIS_RULE_COMPUTE and CLENSHAW_CURTIS_RULE_SET.
</li>
<li>
<a href = "quadrule_fast_test02.m">quadrule_fast_test02.m</a>,
tests CLENSHAW_CURTIS_RULE_COMPUTE.
</li>
<li>
<a href = "quadrule_fast_test03.m">quadrule_fast_test03.m</a>,
tests CLENSHAW_CURTIS_INTEGRATE and CLENSHAW_CURTIS_INTEGRATE_FAST.
</li>
<li>
<a href = "quadrule_fast_test04.m">quadrule_fast_test04.m</a>,
compares GAUSS_LEGENDRE_RULE_COMPUTE and GAUSS_LEGENDRE_RULE_SET.
</li>
<li>
<a href = "quadrule_fast_test05.m">quadrule_fast_test05.m</a>,
tests GAUSS_LEGENDRE_RULE_COMPUTE.
</li>
<li>
<a href = "quadrule_fast_test06.m">quadrule_fast_test06.m</a>,
tests GAUSS_LEGENDRE_INTEGRATE_FAST.
</li>
<li>
<a href = "quadrule_fast_test07.m">quadrule_fast_test07.m</a>,
compares FEJER1_RULE_COMPUTE and FEJER1_RULE_SET.
</li>
<li>
<a href = "quadrule_fast_test08.m">quadrule_fast_test08.m</a>,
tests FEJER1_RULE_COMPUTE.
</li>
<li>
<a href = "quadrule_fast_test09.m">quadrule_fast_test09.m</a>,
tests FEJER1_INTEGRATE_FAST.
</li>
<li>
<a href = "quadrule_fast_test10.m">quadrule_fast_test10.m</a>,
compares FEJER2_RULE_COMPUTE and FEJER2_RULE_SET.
</li>
<li>
<a href = "quadrule_fast_test11.m">quadrule_fast_test11.m</a>,
tests FEJER2_RULE_COMPUTE.
</li>
<li>
<a href = "quadrule_fast_test12.m">quadrule_fast_test12.m</a>,
tests FEJER2_INTEGRATE_FAST.
</li>
<li>
<a href = "f1.m">f1.m</a>,
test integrand function #1.
</li>
<li>
<a href = "f2.m">f2.m</a>,
test integrand function #2.
</li>
<li>
<a href = "f3.m">f3.m</a>,
test integrand function #3.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 06 March 2007.
</i>
<!-- John Burkardt -->
</body>
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</html>