SPARSE_GRID_GL_DATASET
Create GaussLegendre Sparse Grid Dataset
SPARSE_GRID_GL_DATASET
is a MATLAB program which
creates a GaussLegendre sparse grid dataset.
Usage:
sparse_grid_gl_dataset ( dim_num, level_max )
where

dim_num is the spatial dimension, typically between 2 and 10;

level_max is the sparse grid level, typically between 0 and 6,
which controls the number of points
in the grid. The 1D rules used will have order 2^(level_max)+1.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
SPARSE_GRID_GL_DATASET is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
SPARSE_GRID_CC_DATASET,
a MATLAB program which
creates a sparse grid dataset based on ClenshawCurtis rules.
SPARSE_GRID_GL,
a MATLAB library which
can create a GaussLegendre sparse grid.
SPARSE_GRID_GL,
a dataset directory which
contains GaussLegendre sparse grids.
SPARSE_GRID_MIXED_DATASET,
a MATLAB program which
creates a sparse grid dataset based on a mixture of 1D rules.
SPARSE_GRID_OPEN_DATASET,
a MATLAB program which
creates a sparse grid dataset based on
open rules (Fejer 2, GaussPatterson, NewtonCotesOpen).
Reference:

Volker Barthelmann, Erich Novak, Klaus Ritter,
High Dimensional Polynomial Interpolation on Sparse Grids,
Advances in Computational Mathematics,
Volume 12, Number 4, 2000, pages 273288.

Thomas Gerstner, Michael Griebel,
Numerical Integration Using Sparse Grids,
Numerical Algorithms,
Volume 18, Number 34, 1998, pages 209232.

Albert Nijenhuis, Herbert Wilf,
Combinatorial Algorithms for Computers and Calculators,
Second Edition,
Academic Press, 1978,
ISBN: 0125192606,
LC: QA164.N54.

Fabio Nobile, Raul Tempone, Clayton Webster,
A Sparse Grid Stochastic Collocation Method for Partial Differential
Equations with Random Input Data,
SIAM Journal on Numerical Analysis,
Volume 46, Number 5, 2008, pages 23092345.

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

Dennis Stanton, Dennis White,
Constructive Combinatorics,
Springer, 1986,
ISBN: 0387963472,
LC: QA164.S79.
Source Code:
Examples and Tests:
Here are the three quadrature files created by the command
sparse_grid_gl_dataset ( 2, 3 )
You can go up one level to
the MATLAB source codes.
Last revised on 08 October 2007.