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 GaussLegendre, GaussHermite,
GaussPatterson, or a nested variation of GaussHermite rules,
by Florian Heiss and Viktor Winschel.
TESTPACK,
a C library which
defines the Genz test integrand functions.
Author:
Knut Petras
Reference:

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 337340,
ISBN: 9027725144,
LC: QA299.3.N38

Erich Novak, Klaus Ritter,
High dimensional integration of smooth functions over cubes,
Numerische Mathematik,
Volume 75, Number 1, November 1996, pages 7997.

Erich Novak, Klaus Ritter,
Simple Cubature Formulas with High Polynomial Exactness,
Constructive Approximation,
Volume 15, Number 4, December 1999, pages 499522.

Knut Petras,
Fast Calculation of Coefficients in the Smolyak Algorithm,
Numerical Algorithms,
Volume 26, Number 2, February 2001, pages 93109.

Knut Petras,
Smolyak Cubature of Given Polynomial Degree with Few Nodes
for Increasing Dimension,
Numerische Mathematik,
Volume 93, Number 4, February 2003, pages 729753.

Sergey Smolyak,
Quadrature and Interpolation Formulas for Tensor Products of
Certain Classes of Functions,
Doklady Akademii Nauk SSSR,
Volume 4, 1963, pages 240243.
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.
Last revised on 06 August 2019.