SMOLPACK
Multidimensional Quadrature Using Sparse Grids

SMOLPACK, a C library which estimates the integral of a function over a hypercube using a sparse grid, by Knut Petras.

Languages:

SMOLPACK is available in a C version.

Related Programs:

CLENSHAW_CURTIS_RULE, a C library which can set up a Clenshaw Curtis quadrature grid in multiple dimensions.

smolpack_test

SPARSE_GRID_CC, a dataset directory which contains files of the abscissas of sparse grids based on a Clenshaw Curtis rule.

SPARSE_GRID_F2, a dataset directory which contains files of the abscissas of sparse grids based on a Fejer Type 2 rule.

SPARSE_GRID_GP, a dataset directory which contains files of the abscissas of sparse grids based on a Gauss Patterson rule.

SPARSE_GRID_HW, a C library which creates sparse grids based on Gauss-Legendre, Gauss-Hermite, Gauss-Patterson, or a nested variation of Gauss-Hermite rules, by Florian Heiss and Viktor Winschel.

TESTPACK, a C library which defines the Genz test integrand functions.

Author:

Knut Petras

Reference:

1. Alan Genz,
   A Package for Testing Multiple Integration Subroutines,
   in Numerical Integration: Recent Developments, Software and Applications,
   edited by Patrick Keast, Graeme Fairweather,
   Reidel, 1987, pages 337-340,
   ISBN: 9027725144,
   LC: QA299.3.N38
2. Erich Novak, Klaus Ritter,
   High dimensional integration of smooth functions over cubes,
   Numerische Mathematik,
   Volume 75, Number 1, November 1996, pages 79-97.
3. Erich Novak, Klaus Ritter,
   Simple Cubature Formulas with High Polynomial Exactness,
   Constructive Approximation,
   Volume 15, Number 4, December 1999, pages 499-522.
4. Knut Petras,
   Fast Calculation of Coefficients in the Smolyak Algorithm,
   Numerical Algorithms,
   Volume 26, Number 2, February 2001, pages 93-109.
5. Knut Petras,
   Smolyak Cubature of Given Polynomial Degree with Few Nodes for Increasing Dimension,
   Numerische Mathematik,
   Volume 93, Number 4, February 2003, pages 729-753.
6. Sergey Smolyak,
   Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions,
   Doklady Akademii Nauk SSSR,
   Volume 4, 1963, pages 240-243.

Source Code:

• ccsmolyak.c, sparse integration using standard Clenshaw Curtis rules.
• smolyak.c, sparse integration using delayed Clenshaw Curtis rule.
• smolyak.sh, compiles the source code.
• smolpack.h, the include file.