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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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A Novel Approach to the Approximation of Functions with High Number of Variables: Factorized High Dimensional Model Representation (FHDMP)
by
Metin Demiralp
Informatics Institute, Istanbul Technical University, Turkey

Sobol was perhaps the first mathematician who developed an expansion method for the functions of many variables whose numbers may climb to hundreds or thousands and more. The purpose of his method was to construct such a method that the leading terms of the expansion would have been a constant, one argument functions, two argument functions and so on. He had used a unit weight function and confined the approximation region into a unit hypercube. The method has recently been generalized by Rabitz and his group in such a way that the weight function and the geometry of the approximation region have become quite flexible. The Rabitz group applied this new generalized version of the method to many concrete problems coming from the actual problems of physics, chemistry and engineering. The method has been called  High Dimensional Model Representation" (or HDMR as an acronym). However HDMR has had some undesired features in the components of the expansions like the misreflection of the singularity or regularity type behaviors.

The main theme of this presentation is focused on the efforts to cure these undesired features of HDMR. It is mainly based on the factorization of the HDMR expansion via a hidden perturbation expansion. The method is called Factorized High Dimensional Model Representation (or FHDMR as an acronym) and aims to produce a product approximant sequence which is expected to be converging to the function under consideration. Some illustrative applications will also be mentioned in the presentation.

Date received: February 21, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-73.