QUADRATURE_GOLUB_WELSCH
Quadrature Points and Weights, Golub Welsch Method

QUADRATURE_GOLUB_WELSCH is a FORTRAN77 library which illustrates the use of 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 GNU LGPL license.

Languages:

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:

CLENSHAW_CURTIS_RULE, a FORTRAN77 program which defines a Clenshaw Curtis quadrature rule.

QUADRATURE_LEAST_SQUARES, a FORTRAN77 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 FORTRAN77 library which determines the weights of a quadrature rule using the Vandermonde matrix.

QUADRULE, a FORTRAN77 library which defines quadrature rules for 1-dimensional domains.

TOMS655, a FORTRAN77 library which computes the weights for interpolatory quadrature rule;
this library is commonly called IQPACK;
this is a FORTRAN90 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:

• qwgw.f, the source code.
• qwgw.sh, BASH commands to compile the source code.

Examples and Tests:

• qwgw_prb.f, a sample calling program.
• qwgw_prb.sh, BASH commands to compile and run the sample program.
• qwgw_prb_output.txt, the output file.

List of Routines:

• 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 FORTRAN77 source codes.