Create Gauss-Legendre Sparse Grid Dataset

SPARSE_GRID_GL_DATASET is a MATLAB program which creates a Gauss-Legendre sparse grid dataset.


sparse_grid_gl_dataset ( dim_num, level_max )


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


SPARSE_GRID_GL_DATASET is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

SPARSE_GRID_CC_DATASET, a MATLAB program which creates a sparse grid dataset based on Clenshaw-Curtis rules.

SPARSE_GRID_GL, a MATLAB library which can create a Gauss-Legendre sparse grid.

SPARSE_GRID_GL, a dataset directory which contains Gauss-Legendre sparse grids.

SPARSE_GRID_MIXED_DATASET, a MATLAB program which creates a sparse grid dataset based on a mixture of 1D rules.

SPARSE_GRID_OPEN_DATASET, a MATLAB program which creates a sparse grid dataset based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).


  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:

Here are the three quadrature files created by the command

sparse_grid_gl_dataset ( 2, 3 )

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

Last revised on 08 October 2007.