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QUADRATURE_GOLUB_WELSCH\ Quadrature Points and Weights, Golub Welsch Method {#quadrature_golub_welsch-quadrature-points-and-weights-golub-welsch-method align=”center”} ==================================================

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QUADRATURE_GOLUB_WELSCH is a C++ library which illustrates the use of the Golub Welsch technique for computing the points and weights of a Gaussian quadrature rule.

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

QUADRATURE_GOLUB_WELSCH is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs: {#related-data-and-programs align=”center”}

CLENSHAW_CURTIS_RULE, a C++ program which defines a Clenshaw Curtis quadrature rule.

QUADRATURE_LEAST_SQUARES, a C++ library 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, a C++ library which determines the weights of a quadrature rule using the Vandermonde matrix.

QUADRULE, a C++ library which defines quadrature rules for 1-dimensional domains.

TOMS655, a C++ library which computes the weights for interpolatory quadrature rule;\ this library is commonly called IQPACK;\ this is a C version of ACM TOMS algorithm 655.

Reference: {#reference align=”center”}

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: {#source-code align=”center”}

• qwgw.cpp, the source code.
• qwgw.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• qwgw_prb.cpp, a sample calling program.
• qwgw_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• IMTQLX diagonalizes a symmetric tridiagonal matrix.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8VEC_EVEN returns an R8VEC of evenly spaced values.
• R8VEC_PRINT prints an R8VEC.
• SGQF computes knots and weights of a Gauss Quadrature formula.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

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Last revised on 22 February 2014.