chebyshev2_rule


chebyshev2_rule, a MATLAB code which generates a specific Gauss-Chebyshev type 2 quadrature rule, based on user input.

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

The Gauss-Chevbyshev type 2 quadrature rule is used as follows:

        Integral ( A <= x <= B ) f(x)  sqrt ( ( x - A ) * ( B - x ) ) dx
      
is to be approximated by
        Sum ( 1 <= i <= order ) w(i) * f(x(i))
      

Usage:

chebyshev2_rule ( order, a, b, 'filename' )
where

Licensing:

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

Languages:

chebyshev2_rule is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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chebyshev2_rule_test

lenshaw_curtis_rule, a MATLAB code which defines a clenshaw curtis quadrature rule.

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gen_laguerre_rule, a MATLAB code which can compute and print a generalized gauss-laguerre quadrature rule.

hermite_rule, a MATLAB code which can compute and print a gauss-hermite quadrature rule.

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power_rule, a MATLAB code which constructs a power rule, that is, a product quadrature rule from identical 1d factor rules.

quadrature_rules_chebyshev2, a dataset directory which contains triples of files defining standard gauss-chebyshev type 2 quadrature rules.

quadrule, a MATLAB code which defines 1-dimensional quadrature rules.

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Reference:

  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.
  3. 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 399-415.
  4. Jaroslav Kautsky, Sylvan Elhay,
    Calculation of the Weights of Interpolatory Quadratures,
    Numerische Mathematik,
    Volume 40, 1982, pages 407-422.
  5. Roger Martin, James Wilkinson,
    The Implicit QL Algorithm,
    Numerische Mathematik,
    Volume 12, Number 5, December 1968, pages 377-383.
  6. Arthur Stroud, Don Secrest,
    Gaussian Quadrature Formulas,
    Prentice Hall, 1966,
    LC: QA299.4G3S7.

Source Code:


Last revised on 10 December 2018.