laguerre_rule

laguerre_rule, a FORTRAN77 code which generates a specific Gauss-Laguerre quadrature rule, based on user input.

The rule is written to three files for easy use as input to other programs.

The Gauss-Laguerre quadrature rule is used as follows:

        Integral ( a <= x < +oo ) exp ( - b * ( x - a ) ) f(x) dx

is to be approximated by

        Sum ( 1 <= i <= order ) w(i) * f(x(i))

laguerre_rule order a b filename

where

order is the number of points in the quadrature rule.
a is the left endpoint. Typically this is 0.
b is the scale factor. Typically this is 1.
filename specifies the output filenames: filename_w.txt, filename_x.txt, and filename_r.txt, containing the weights, abscissas, and interval limits.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

laguerre_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

ccn_rule, a FORTRAN77 program which defines a nested Clenshaw Curtis quadrature rule.

clenshaw_curtis_rule, a FORTRAN77 program which defines a Clenshaw Curtis quadrature rule.

HERMITE_RULE, a FORTRAN77 program which can compute and print a Gauss-Hermite quadrature rule.

LAGUERRE_EXACTNESS, a FORTRAN77 program which checks the polynomial exactness of a Gauss-Laguerre quadrature rule.

LAGUERRE_POLYNOMIAL, a FORTRAN77 library which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.

LAGUERRE_TEST_INT, a FORTRAN77 library which defines test integrands for integration over [A,+oo).

LEGENDRE_RULE, a FORTRAN77 program which computes a Gauss-Legendre quadrature rule.

LEGENDRE_RULE_FAST, a FORTRAN77 program which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.

QUADRULE, a FORTRAN77 library which contains 1-dimensional quadrature rules.

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ACM Transactions on Mathematical Software,
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Volume 40, 1982, pages 407-422.
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Numerische Mathematik,
Volume 12, Number 5, December 1968, pages 377-383.
Philip Rabinowitz, George Weiss,
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Volume 13, Number 68, October 1959, pages 285-294.
Arthur Stroud, Don Secrest,
Gaussian Quadrature Formulas,
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Last revised on 18 October 2023.