SPARSE_GRID_PURE
Sparse Grids Using a Single Factor

SPARSE_GRID_PURE is 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_GRID_PURE is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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).
• sparse_grid_cc_se_size.m Clenshaw Curtis Slow Exponential Growth.
• sparse_grid_cfn_e_size.m Closed Fully Nested, Exponential Growth.
• sparse_grid_f2_se_size.m Fejer Type 2 Slow Growth.
• sparse_grid_gp_se_size.m Gauss Patterson, Slow Growth.
• sparse_grid_ofn_e_size.m Open Fully Nested, Exponential Growth.
• sparse_grid_onn_e_size.m Open Non Nested, Exponential Growth.
• sparse_grid_onn_l_size.m Open Non Nested, Linear Growth.
• sparse_grid_own_e_size.m Open Weakly Nested, Exponential Growth.
• sparse_grid_own_l_size.m Open Weakly Nested, Linear Growth.
• sparse_grid_own_ls_size.m Open Weakly Nested, Linear (Slow) Growth.
• timestamp.m prints the current YMDHMS date as a time stamp.

Examples and Tests:

• sparse_grid_pure_test.m, a sample calling program.
• sparse_grid_pure_test01.m, tests SPARSE_GRID_CC_SE_SIZE.
• sparse_grid_pure_test02.m, tests SPARSE_GRID_CFN_E_SIZE.
• sparse_grid_pure_test03.m, tests SPARSE_GRID_F2_SE_SIZE.
• sparse_grid_pure_test04.m, tests SPARSE_GRID_GP_SE_SIZE.
• sparse_grid_pure_test05.m, tests SPARSE_GRID_OFN_E_SIZE.
• sparse_grid_pure_test06.m, tests SPARSE_GRID_ONN_E_SIZE.
• sparse_grid_pure_test07.m, tests SPARSE_GRID_ONN_L_SIZE.
• sparse_grid_pure_test08.m, tests SPARSE_GRID_OWN_E_SIZE.
• sparse_grid_pure_test09.m, tests SPARSE_GRID_OWN_L_SIZE.
• sparse_grid_pure_test10.m, tests SPARSE_GRID_OWN_LS_SIZE.
• sparse_grid_pure_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.