sparse_count
sparse_count,
a MATLAB code which
contains routines for the analysis and construction of sparse grids
in which a fixed family of 1D quadrature rules is used for all spatial
dimensions.
By contrast, library SPARSE_GRID_MIXED allows different rules to
be used in different dimensions.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
sparse_count is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
sparse_count_test
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:

comp_next.m
computes the compositions of the integer N into K parts.

cc_se_size.m
Clenshaw Curtis Slow Exponential Growth.

cfn_e_nvec_from_lvec.m
Closed Fully Nested, Exponential Growth,
return 1D rule sizes based on 1D rule levels.

cfn_e_size.m
Closed Fully Nested, Exponential Growth,
merge repeated points.

cfn_e_size_total.m
Closed Fully Nested, Exponential Growth,
don't merge repeated points.

f2_se_size.m
Fejer Type 2 Slow Growth.

gp_se_size.m
Gauss Patterson, Slow Growth.

ofn_e_size.m
Open Fully Nested, Exponential Growth.

onn_e_size.m
Open Non Nested, Exponential Growth.

onn_l_size.m
Open Non Nested, Linear Growth.

own_e_size.m
Open Weakly Nested, Exponential Growth.

own_l2_size.m
Open Weakly Nested, Linear 2 Growth.

own_o_size.m
Open Weakly Nested, Odd Growth.
Last revised on 11 January 2021.