jacobi_rule
jacobi_rule,
an Octave code which
generates a specific GaussJacobi quadrature rule,
based on user input.
The rule is written to three files for easy use as input
to other programs.
The GaussJacobi quadrature rule is used as follows:
Integral ( A <= x <= B ) (Bx)^alpha (xA)^beta f(x) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
a b
Usage:
jacobi_rule ( order, alpha, beta, a, b, 'filename' )
where

order is the number of points in the quadrature rule.

alpha is the exponent of (Bx), which must be greater than 1.

beta is the exponent of (xA), which must be greater than 1.

a is the left endpoint;

b is the right endpoint.

'filename' specifies how the rule is to be reported:
filename_w.txt,
filename_x.txt, and filename_r.txt,
containing the weights, abscissas, and interval limits.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
jacobi_rule is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version and
an Octave version.
Related Data and Programs:
jacobi_rule_test
jacobi_polynomial,
a MATLAB code which
evaluates the Jacobi polynomial and associated functions.
Reference:

Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0486612724,
LC: QA47.A34.

Philip Davis, Philip Rabinowitz,
Methods of Numerical Integration,
Second Edition,
Dover, 2007,
ISBN: 0486453391,
LC: QA299.3.D28.

Sylvan Elhay, Jaroslav Kautsky,
Algorithm 655:
IQPACK,
FORTRAN Subroutines for the Weights of Interpolatory Quadrature,
ACM Transactions on Mathematical Software,
Volume 13, Number 4, December 1987, pages 399415.

Jaroslav Kautsky, Sylvan Elhay,
Calculation of the Weights of Interpolatory Quadratures,
Numerische Mathematik,
Volume 40, 1982, pages 407422.

Roger Martin, James Wilkinson,
The Implicit QL Algorithm,
Numerische Mathematik,
Volume 12, Number 5, December 1968, pages 377383.

Arthur Stroud, Don Secrest,
Gaussian Quadrature Formulas,
Prentice Hall, 1966,
LC: QA299.4G3S7.
Source Code:
Last revised on 25 September 2022.