A Factorized High Dimensional Model Representation on the Partitioned Random Discrete Data

Abstract

The main purpose of this work is to obtain the general structure of a product type of multivariate function when the values of the function are given randomly at the nodes of a hyperprism. When the dimensionality of multivariate interpolation and the number of the data sets increase unboundedly, many problems can be encountered in the standard numerical methods. Factorized High Dimensional Model Representation (FHDMR) is used to obtain the general structure of this given multivariate function. The components of FHDMR are determined by using the components of the Generalized High Dimensional Model Representation (GHDMR).The given random discrete data is partitioned by GHDMR method. This partitioned data produces a structure for the multivariate function by using single variable Lagrange interpolation formula including only the constant term and the univariate terms of the GHDMR components. Finally, a general structure is obtained via FHMDR by using these components. By this way, the multidimensionality of a multivariate interpolation is approximated by lower dimensional interpolations like univariate ones. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)