sparse_grid_hermite, a MATLAB code which constructs sparse grids based on 1D GaussHermite rules.
Sparse grids are more naturally constructed from a nested family of quadrature rules. GaussHermite rules are not nested, but have higher accuracy. Thus, there can be a tradeoff. If we compare two sparse grids of the same "level", one using GaussHermite rules and the other a nested rule, then the GaussHermite sparse grid will have higher accuracy...but also a significantly greater number of points. When measuring efficiency, we really need to balance the cost in quadrature points against the accuracy, and so it is not immediately obvious which choice is best!
To slightly complicate matters, GaussHermite rules are very weakly nested, in that the rules of odd order all include the abscissa value X=0.0. A sparse grid constructed from GaussHermite rules will thus have to keep track of this minor point as well.
Here is a table showing the number of points in a sparse grid based on GaussHermite rules, indexed by the spatial dimension, and by the "level", which is simply an index for the family of sparse grids.
DIM:  1  2  3  4  5  6 

LEVEL_MAX  
0  1  1  1  1  1  1 
1  3  5  7  9  11  13 
2  7  22  37  57  81  109 
3  15  75  161  289  471  713 
4  31  224  608  1268  2341  3953 
5  63  613  2070  4994  10367  19397 
6  127  1570  6507  18076  41957  86522 
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
sparse_grid_hermite is available in a C++ version and a FORTRAN90 version and a MATLAB version.
sparse_grid_cc, a MATLAB code which computes sparse grids based on a clenshawcurtis rule.
sparse_grid_composite, a MATLAB code which creates sparse grids based on 1d composite rules (currently only of order 1).
sparse_grid_gl, a MATLAB code which computes a sparse grid based on 1d gausslegendre rules.
sparse_grid_hermite, a dataset directory which contains sparse grids based on a gausshermite rule.
sparse_grid_hw, a MATLAB code which creates sparse grids based on gausslegendre, gausshermite, gausspatterson, or a nested variation of gausshermite rules, by florian heiss and viktor winschel.
spquad, a MATLAB code which computes the points and weights of a sparse grid quadrature rule for a multidimensional integral, based on the clenshawcurtis quadrature rule, by greg von winckel.
toms847, a MATLAB code which uses sparse grids to carry out multilinear hierarchical interpolation. it is commonly known as spinterp, and is by andreas klimke.
