sparse_grid_hw


sparse_grid_hw, a MATLAB code which can compute sparse grids for multidimensional integration, based on 1D rules for the unit interval with unit weight function, or for the real line with the Gauss-Hermite weight function. The original version of the code is by Florian Heiss and Viktor Winschel.

Four built-in 1D families of quadrature rules are supplied, and the user can extend the package by supplying any family of 1D quadrature rules.

The built-in families are identified by a 3-letter key which is also the name of the function that returns members of the family:

The user can build new sparse grids by supplying a 1D quadrature family. Examples provided include:

Licensing:

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

Languages:

sparse_grid_hw is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

sparse_grid_hw_test

grid_display, a MATLAB code which displays a 2d or 3d grid or sparse grid.

nint_exactness_mixed, a MATLAB code which measures the polynomial exactness of a multidimensional quadrature rule based on a mixture of 1d quadrature rule factors.

product_rule, a MATLAB code which constructs a product quadrature rule from identical 1d factor rules.

quad_rule, a MATLAB code which defines quadrature rules for various intervals and weight functions.

sparse_grid_cc, a MATLAB code which defines a multidimensional sparse grid based on a 1d Clenshaw Curtis rule.

sparse_grid_gl, a MATLAB code which creates sparse grids based on Gauss-Legendre rules.

sparse_grid_hermite, a MATLAB code which creates sparse grids based on Gauss-Hermite rules.

sparse_grid_laguerre, a MATLAB code which creates sparse grids based on Gauss-Laguerre rules.

spinterp, a MATLAB code which carries out piecewise multilinear hierarchical sparse grid interpolation; an earlier version of this software is ACM TOMS algorithm 847, by Andreas Klimke;

spquad, a MATLAB code which computes the points and weights of a sparse grid quadrature rule for a multidimensional integral, based on the Clenshaw-Curtis quadrature rule, by Greg von Winckel.

Author:

Original MATLAB code by Florian Heiss and Viktor Winschel.

Reference:

Source Code:


Last revised on 20 March 2019.