GEGENBAUER_RULE, a MATLAB program which generates a specific Gauss-Gegenbauer quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss-Gegenbauer quadrature rule is used as follows:
Integral ( A <= x <= B ) ((x-A)(B-X))^alpha f(x) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
where alpha is a real parameter greater than -1.
gegenbauer_rule ( order, alpha, a, b, 'filename' )where
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
GEGENBAUER_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
ALPERT_RULE, a MATLAB library which can set up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
CCN_RULE, a MATLAB program which defines a nested Clenshaw Curtis quadrature rule.
CHEBYSHEV1_RULE, a MATLAB program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a MATLAB program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE, a MATLAB program which defines a Clenshaw Curtis quadrature rule.
GEGENBAUER_CC, a MATLAB library which estimates the Gegenbauer weighted integral of a function f(x) using a Clenshaw-Curtis approach.
GEGENBAUER_EXACTNESS, a MATLAB program which tests the monomial exactness of Gauss-Gegenbauer quadrature rules.
GEGENBAUER_POLYNOMIAL, a MATLAB library which evaluates the Gegenbauer polynomial and associated functions.
GEN_HERMITE_RULE, a MATLAB program which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, a MATLAB program which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a MATLAB program which can compute and print a Gauss-Hermite quadrature rule.
JACOBI_RULE, a MATLAB program which can compute and print a Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a MATLAB program which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a MATLAB program which computes a Gauss-Legendre quadrature rule.
LINE_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.
PATTERSON_RULE, a MATLAB program which computes a Gauss-Patterson quadrature rule.
POWER_RULE, a MATLAB program which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
QUADRATURE_RULES_GEGENBAUER, a dataset directory which contains triples of files defining Gauss-Gegenbauer quadrature rules.
QUADRULE, a MATLAB library which contains 1-dimensional quadrature rules.
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