toms699

toms699, a Fortran77 code which implements ACM toms Algorithm 699, which is an implementation of Patterson's adapative quadrature formulas.

toms699 is ACM toms Algorithm 699. The text of the original Fortran77 version is available online through ACM: https://www.acm.org/pubs/calgo or NETLIB: https://www.netlib.org/toms/index.html.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

toms699 is available in a Fortran77 version.

Related Data and Programs:

toms699_test

kronrod_rule, a Fortran77 library which can compute a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.

patterson_rule, a Fortran90 program which computes a 1D Gauss-Patterson quadrature rule.

QUADRATURE_RULES_PATTERSON, a dataset directory which contains Gauss-Patterson quadrature rules for the interval [-1,+1].

SANDIA_RULES, a Fortran90 library which produces 1D quadrature rules of Chebyshev, Clenshaw Curtis, Fejer 2, Gegenbauer, generalized Hermite, generalized Laguerre, Hermite, Jacobi, Laguerre, Legendre and Patterson types.

Author:

Fred Krogh, Van Snyder

Reference:

1. Fred Krogh, Van Snyder,
   Algorithm 699: a new representation of Patterson's quadrature formula,
   ACM Transactions on Mathematical Software,
   Volume 17, Number 4, December 1991, pages 457-461.
2. Thomas Patterson,
   Algorithm 468: Algorithm for Automatic Numerical Integration Over a Finite Interval,
   Communications of the ACM,
   Volume 16, Number 11, November 1973, pages 694-699.
3. Thomas Patterson,
   An algorithm for generating interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions,
   Transactions on Mathematical Software,
   Volume 15, Number 2, June 1989, pages 123-136.
4. Thomas Patterson,
   Algorithm 672: EXTEND: generation of interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions,
   Transactions on Mathematical Software,
   Volume 15, Number 2, June 1989, pages 137-143.

Source Code:

• toms699.f, the source code;
• toms699.sh, commands to compile the source code;