SPARSE_COUNT
Sparse Grids Using a Single Factor


SPARSE_COUNT 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_COUNT 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:

Examples and Tests:

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


Last revised on 25 May 2014.