A factorized high dimensional model representation on the nodes of a finite hyperprismatic regular grid

Tunga M., Demiralp M.

APPLIED MATHEMATICS AND COMPUTATION, vol.164, no.3, pp.865-883, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 164 Issue: 3
  • Publication Date: 2005
  • Doi Number: 10.1016/j.amc.2004.06.056
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.865-883
  • Istanbul Technical University Affiliated: No


When the values of a multivariate function f(x(1),...,x(N)), having N independent variables like x(1),...,x(N) are given at the nodes of a cartesian, product set in the space of the independent variables and ail interpolation problem is defined to find out the analytical structure of this function some difficulties arise in the standard methods due to the multidimensionality of the problem. Here, the main purpose is to partition this multivariate data into low-variate data and to obtain the analytical structure of the multivariate function by using this partitioned data. High dimensional model representation (HDMR) is used for these types of problems. However, if HDMR requires all components, which means 2(N) number of components, to get a desired accuracy then factorized high dimensional model representation (FHDMR) can be used. This method uses the components of HDMR. This representation is needed when the sought multivariate function has a multiplicative nature. In this work we introduce how to utilize FHDMR for these problems and present illustrative examples. (c) 2004 Elsevier Inc. All rights reserved.