SPARSE_COUNT\
Sparse Grids Using a Single Factor {#sparse_count-sparse-grids-using-a-single-factor align=”center”}
==================================
SPARSE_COUNT is a C++ 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 MIXED allows different rules to be used in
different dimensions.
Licensing: {#licensing align=”center”}
The computer code and data files described and made available on this
web page are distributed under the GNU LGPL
license.
Languages: {#languages align=”center”}
SPARSE_COUNT is available in a C++
version and a FORTRAN90
version and a MATLAB
version.
MIXED, a
library which creates a sparse grid dataset based on a mixed set of 1D
factor rules.
Reference: {#reference align=”center”}
- 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.
- Thomas Gerstner, Michael Griebel,\
Numerical Integration Using Sparse Grids,\
Numerical Algorithms,\
Volume 18, Number 3-4, 1998, pages 209-232.
- Albert Nijenhuis, Herbert Wilf,\
Combinatorial Algorithms for Computers and Calculators,\
Second Edition,\
Academic Press, 1978,\
ISBN: 0-12-519260-6,\
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 2309-2345.
- Sergey Smolyak,\
Quadrature and Interpolation Formulas for Tensor Products of Certain
Classes of Functions,\
Doklady Akademii Nauk SSSR,\
Volume 4, 1963, pages 240-243.
- Dennis Stanton, Dennis White,\
Constructive Combinatorics,\
Springer, 1986,\
ISBN: 0387963472,\
LC: QA164.S79.
Source Code: {#source-code align=”center”}
Examples and Tests: {#examples-and-tests align=”center”}
List of Routines: {#list-of-routines align=”center”}
- CC_S_SIZE: Clenshaw Curtis Slow Exponential Growth.
- CFN_E_SIZE; Closed Fully Nested, Exponential Growth.
- COMP_NEXT computes the compositions of the integer N into K
parts.
- F2_S_SIZE: Fejer Type 2 Slow Growth.
- GP_S_SIZE: Gauss Patterson, Slow Growth.
- I4_CHOOSE computes the binomial coefficient C(N,K).
- OFN_E_SIZE: Open Fully Nested, Exponential Growth.
- ONN_E_SIZE: Open Non Nested, Exponential Growth.
- ONN_L_SIZE: Open Non Nested, Linear Growth.
- OWN_E_SIZE: Open Weakly Nested, Exponential Growth.
- OWN_L2_SIZE: Open Weakly Nested, Linear 2 Growth.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to the C++ source codes.
Last revised on 25 April 2014.