quadrature_golub_welsch

quadrature_golub_welsch, an Octave code which uses the Golub Welsch technique for computing the points and weights of a Gaussian quadrature rule.

Licensing:

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

Languages:

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

Related Data and Programs:

quadrature_golub_welsch_test

clenshaw_curtis_rule, an Octave code which defines a Clenshaw Curtis quadrature rule.

quadrature_least_squares, an Octave code which computes weights for "sub-interpolatory" quadrature rules, that is, it estimates integrals by integrating a polynomial that approximates the function data in a least squares sense.

quadrature_weights_vandermonde, an Octave code which determines the weights of a quadrature rule using the Vandermonde matrix.

quad_rule, an Octave code which defines quadrature rules for 1-dimensional domains.

toms655, an Octave code which computes the weights for interpolatory quadrature rule;
this library is commonly called iqpack();
this is a version of ACM TOMS algorithm 655.

Reference:

1. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.
2. 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.
3. Jaroslav Kautsky, Sylvan Elhay,
   Calculation of the Weights of Interpolatory Quadratures,
   Numerische Mathematik,
   Volume 40, 1982, pages 407-422.

Source Code:

• imtqlx.m, diagonalizes a symmetric tridiagonal matrix.
• r8_sign.m, returns the sign of an R8.
• r8mat_print.m, prints an R8MAT.
• r8mat_print_some.m, prints some of an R8MAT.
• r8vec_print.m, prints an R8VEC.
• sgqf.m, computes knots and weights of a Gauss Quadrature formula.