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<html>
<head>
<title>
TOMS726 - Orthogonal Polynomials and Quadrature Rules
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS726 <br> Orthogonal Polynomials and Quadrature Rules
</h1>
<hr>
<p>
<b>TOMS726</b>
is a FORTRAN90 library which
computes recursion relationships for various families of
orthogonal polynomials, as well as the abscissas and weights of
related quadrature rules.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS726</b> is available in
<a href = "../../f77_src/toms726/toms726.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms726/toms726.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f77_src/toms655/toms655.html">
TOMS655</a>,
a FORTRAN77 library which
computes the weights for interpolatory quadrature rules.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
William Cody, Kenneth Hillstrom,<br>
Chebyshev Approximations for the Natural Logarithm of the
Gamma Function,<br>
Mathematics of Computation,<br>
Volume 21, Number 98, April 1967, pages 198-203.
</li>
<li>
Walter Gautschi,<br>
On Generating Orthogonal Polynomials,<br>
SIAM Journal on Scientific and Statistical Computing,<br>
Volume 3, Number 3, 1982, pages 289-317.
</li>
<li>
Walter Gautschi,<br>
Algorithm 726:
ORTHPOL - A Package of Routines for Generating Orthogonal
Polynomials and Gauss-Type Quadrature Rules,<br>
ACM Transactions on Mathematical Software,<br>
Volume 20, Number 1, March 1994, pages 21-62.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms726.f90">toms726.f90</a>, the source code.
</li>
<li>
<a href = "toms726.sh">toms726.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms726_prb.f90">toms726_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "toms726_prb.sh">toms726_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "toms726_prb_output.txt">toms726_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ALGA_R4</b> evaluates the logarithm of the gamma function.
</li>
<li>
<b>ALGA_R8</b> evaluates the logarithm of the gamma function.
</li>
<li>
<b>CHEB_R4</b> generates recursion coefficients ALPHA and BETA.
</li>
<li>
<b>CHEB_R8</b> generates recursion coefficients ALPHA and BETA.
</li>
<li>
<b>CHRI_R4</b> implements the Christoffel or generalized Christoffel theorem.
</li>
<li>
<b>CHRI_R8</b> implements the Christoffel or generalized Christoffel theorem.
</li>
<li>
<b>FEJER_R4</b> generates a Fejer quadrature rule.
</li>
<li>
<b>FEJER_R8</b> generates a Fejer quadrature rule.
</li>
<li>
<b>GAMMA_R4</b> evaluates the gamma function for real positive X.
</li>
<li>
<b>GAMMA_R8</b> evaluates the gamma function for real positive argument.
</li>
<li>
<b>GAUSS_R4</b> generates an N-point Gaussian quadrature formula.
</li>
<li>
<b>GAUSS_R8</b> generates an N-point Gaussian quadrature formula.
</li>
<li>
<b>GCHRI_R4</b> implements the generalized Christoffel theorem.
</li>
<li>
<b>GCHRI_R8</b> implements the generalized Christoffel theorem.
</li>
<li>
<b>KERN_R4</b> generates the kernels in the Gauss quadrature remainder term.
</li>
<li>
<b>KERN_R8</b> generates the kernels in the Gauss quadrature remainder term.
</li>
<li>
<b>KNUM_R4</b> integrates certain rational polynomials.
</li>
<li>
<b>KNUM_R8</b> is a double-precision version of the routine KNUM_R4.
</li>
<li>
<b>LANCZ_R4</b> applies Stieltjes's procedure, using the Lanczos method.
</li>
<li>
<b>LANCZ_R8</b> is a double-precision version of the routine LANCZ_R4.
</li>
<li>
<b>LOB_R4</b> generates a Gauss-Lobatto quadrature rule.
</li>
<li>
<b>LOB_R8</b> generates a Gauss-Lobatto quadrature rule.
</li>
<li>
<b>MCCHEB_R4</b> is a multiple-component discretized modified Chebyshev algorithm.
</li>
<li>
<b>MCCHEB_R8</b> is a double-precision version of the routine MCCHEB_R4.
</li>
<li>
<b>MCDIS_R4</b> is a multiple-component discretization procedure.
</li>
<li>
<b>MCDIS_R8</b> is a double-precision version of the routine MCDIS_R4.
</li>
<li>
<b>NU0HER</b> estimates a starting index for recursion with the Hermite measure.
</li>
<li>
<b>NU0JAC</b> estimates a starting index for recursion with the Jacobi measure.
</li>
<li>
<b>NU0LAG</b> estimates a starting index for recursion with the Laguerre measure.
</li>
<li>
<b>QGP_R4</b> is a general-purpose discretization routine.
</li>
<li>
<b>QGP_R8</b> is a double-precision version of the routine QGP_R4.
</li>
<li>
<b>RADAU_R4</b> generates a Gauss-Radau quadrature formula.
</li>
<li>
<b>RADAU_R8</b> generates a Gauss-Radau quadrature formula.
</li>
<li>
<b>RECUR_R4</b> generates recursion coefficients for orthogonal polynomials.
</li>
<li>
<b>RECUR_R8</b> is a double-precision version of the routine RECUR_R4.
</li>
<li>
<b>STI_R4</b> applies Stieltjes's procedure.
</li>
<li>
<b>STI_R8</b> is a double-precision version of the routine STI_R4.
</li>
<li>
<b>SYMTR_R4</b> maps T in [-1,1] to X in (-oo,oo).
</li>
<li>
<b>SYMTR_R8</b> maps T in [-1,1] to X in (-oo,oo).
</li>
<li>
<b>T_FUNCTION</b> solves Y = T * log ( T ) for T, given nonnegative Y.
</li>
<li>
<b>TR_R4</b> maps T in [-1,1] to X in [0,oo).
</li>
<li>
<b>TR_R8</b> maps T in [-1,1] to X in [0,oo).
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 10 January 2008.
</i>
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