SPARSE_COUNT
Sparse Grids Using a Single Factor

SPARSE_COUNT, a MATLAB library 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

SPARSE_GRID_MIXED, a library which creates a sparse grid dataset based on a mixed set of 1D factor rules.

Reference:

1. Volker Barthelmann, Erich Novak, Klaus Ritter,
   High Dimensional Polynomial Interpolation on Sparse Grids,
   Advances in Computational Mathematics,
   Volume 12, Number 4, 2000, pages 273-288.
2. Thomas Gerstner, Michael Griebel,
   Numerical Integration Using Sparse Grids,
   Numerical Algorithms,
   Volume 18, Number 3-4, 1998, pages 209-232.
3. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.
4. 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 2309-2345.
5. Sergey Smolyak,
   Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions,
   Doklady Akademii Nauk SSSR,
   Volume 4, 1963, pages 240-243.
6. 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.
• i4_choose.m computes the binomial coefficient C(N,K).
• 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.
• timestamp.m prints the current YMDHMS date as a time stamp.