Abstract
In multivariate interpolation problems, increase in both the number of independent variables of the sought function and the number of nodes appearing in the data set causes computational and mathematical difficulties. It may be a better way to deal with less variate partitioned data sets instead of an N-dimensional data set in a multivariate interpolation problem. New algorithms such as high-dimensional model representation (HDMR), generalized HDMR, factorized HDMR, hybrid HDMR are developed or rearranged for these types of problems. Up to now, the efficiency of the methods in mathematical sense was discussed in several papers. In this work, the efficiency of these methods in computational sense will be discussed. This investigation will be done by using several numerical implementations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Sobol IM (1993) Sensitivity estimates for nonlinear mathematical models. Math. Model. and Comput. Exp. (MMCE) 1:407
Rabitz H, Alış Ö (1999) General foundations of high dimensional model representations. J. Math. Chem. 25:197–233
Alış Ö, Rabitz H (2001) Efficient implementation of high dimensional model representations. J. Math. Chem. 29:127–142
Li G, Rosenthal C, Rabitz H (2001) High dimensional model representations. J. Math. Chem. A 105:7765–7777
Demiralp M (2003) High dimensional model representation and its varieties. Math. Res. 9:146–159
Tunga B, Demiralp M (2003) Hybrid high dimensional model representation approximants and their utilization in applications. Math. Res. 9:438–446
Demiralp M, Tunga MA (2001) High dimensional model representation of multivariate interpolation via hypergrids. In: the Sixteenth International Symposium on Computer and Information Sciences, pp 416–423
Tunga MA, Demiralp M (2003) Data partitioning via generalized high dimensional model representation (GHDMR) and multivariate interpolative applications. Math. Res. 9:447–462
Tunga MA, Demiralp M (2004) A factorized high dimensional model representation on the partitioned random discrete data. Appl. Num. Anal. Comp. Math. 1:231–241
Tunga MA, Demiralp M (2005) A factorized high dimensional model representation on the nodes of a finite hyperprismatic regular grid. Appl. Math. and Comput. 164:865–883
Tunga MA, Demiralp M (2006) Hybrid high dimensional model representation (HHDMR) on the partitioned data. J. Comput. Appl. Math. 185:107–132
Oevel W, Postel F, Wehmeier S, Gerhard J (2000) The MuPAD tutorial. Springer, New York
Deitel HM, Deitel PJ, Nieto TR, McPhie DC (2001) Perl how to program. Prentice Hall, Englewood Cliffs
Zemanian AH (1987) Distribution theory and transform analysis, An introduction to generalized functions, with applications. Dover Publications Inc., New York
Buchanan JL, Turner PR (1992) Numerical methods and analysis. McGraw-Hill, New York
Acknowledgment
The second author is grateful to Turkish Academy of Sciences and both authors thank WSEAS for their supports.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media LLC
About this chapter
Cite this chapter
Tunga, M.A., Demiralp, M. (2009). Computational complexity investigations for high-dimensional model representation algorithms used in multivariate interpolation problems. In: Mastorakis, N., Sakellaris, J. (eds) Advances in Numerical Methods. Lecture Notes in Electrical Engineering, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76483-2_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-76483-2_2
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-76482-5
Online ISBN: 978-0-387-76483-2
eBook Packages: EngineeringEngineering (R0)