Algorithm 847: Spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB

ACM Transactions on Mathematical Software

Volumn 31, Issue 4, 2005, Pages 561-579

  Klimke, Andreas ^a   Wohlmuth, Barbara ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Multivariate interpolation; Smolyak algorithm; Sparse grids

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DISTRIBUTED COMPUTER SYSTEMS; HIERARCHICAL SYSTEMS;

MULTIVARIATE INTERPOLATION; SMOLYAK ALGORITHM; SPARSE GRIDS;

INTERPOLATION;

EID: 33745213726     PISSN: 00983500     EISSN: 00983500     Source Type: Journal    
DOI: 10.1145/1114268.1114275     Document Type: Conference Paper

References (15)

1. BARTHELMANN, V., NOVAK, E., AND RITTER, K. 2000. High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 12, 4, 273-288.
2. BUNGARTZ, H.-J. 1992. Dünne Gitter und deren Anwendung bei der adaptiven Lösung der drei-dimensionalen Poissongleichung. Ph.D. dissertation. Technische Universität München, Munich, Germany.
3. BUNGARTZ, H.-J. 1998. Finite Elements of Higher Order on Sparse Grids. Shaker Verlag, Aachen, Germany.
4. BUNGARTZ, H.-J. AND GRIEBEL, M. 2004. Sparse grids. Acta. Numerica 13, 147-269.
5. CLENSHAW, C. W. AND CURTIS, A. R. 1960. A method for numerical integration on an automatic computer. Numer. Math. 2, 197-205.
6. GENZ, A. C. 1987. A package for testing multiple integration subroutines. In Numerical Integration, P. Keast and G. Fairweather, Eds. Kluwer, Dordrecht, The Netherlands, 337-340.
7. KLIMKE, A. 2006. Uncertainty modeling using sparse grids. PhD dissertation. Universität Stuttgard, Germany.
8. KLIMKE, A., WILLNER, K., AND WOHLMUTH, B. 2004. Uncertainty modeling using fuzzy arithmetic based on sparse grids: Applications to dynamic systems. Int. J. Uncertaint. Fuzz. Knowl.-Based Syst. 12, 6, 745-759.
9. KLIMKE, A. AND WOHLMUTH, B. 2005. Computing expensive multivariate functions of fuzzy numbers using sparse grids. Fuzz. Sets Syst. 154, 3, 432-453.
10. NOVAK, E. AND RITTER, K. 1996. High-dimensional integration of smooth functions over cubes. Numer. Math. 75, 1, 79-97.
11. SCHREIBER, A. 2000. Smolyak's method for multivariate interpolation. Ph.D. dissertation. Georg-August-Universität Göttingen, Göttingen, Germany.
12. SHAMPINE, L. F. AND REICHELT, M. W. 1997. The MATLAB ODE suite. SIAM J. Sci. Comput. 18, 1, 1-22.
13. SMOLYAK, S.A. 1963. Quadrature and interpolation formulas for tensor products of certain classes of functions. Soviet Math. Dokl. 4, 240-243.
14. SPRENGEL, F. 1997. Interpolation and wavelets on sparse Gauss-Chebyshev grids. In Multivariate Approximation, W. Haussmann et al., Eds. Mathematical Research, vol. 101. Akademie Verlag, Berlin, Germany, 269-286.
15. SPRENGEL, F. 1998. Periodic interpolation and wavelets on sparse grids. Numer. Algorith. 17, 1-2, 147-169.