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Combined small scale high dimensional model representation

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Abstract

Nowadays the utilization of High Dimensional Model Representation (HDMR), which is an algorithm for approximating multivariate functions, is becoming more pervasive in the applications of approximation theory. This extensive usage motivates new works on HDMR, to get better solutions while approximating to the multivariate functions. One of them is recently developed “Combined Small Scale High Dimensional Model Representation (CSSHDMR)". This new scheme not only optimises HDMR results but also provides good approximation with less terms than HDMR does. This paper presents the theory and the numerical results of the new method and shows that it is possible to apply approximation to multivariate functions by keeping only constant term of HDMR. From this aspect CSSHDMR can be used in any scientific problem which includes multivariate functions, from chemistry to statistics.

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Authors and Affiliations

  1. Computational Science and Engineering Program, Group for Science and Methods of Computation, Informatics Institute, İstanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Evrim Korkmaz Özay & Metin Demiralp

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  1. Evrim Korkmaz Özay
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  2. Metin Demiralp
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Correspondence to Evrim Korkmaz Özay.

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Özay, E.K., Demiralp, M. Combined small scale high dimensional model representation. J Math Chem 50, 2023–2042 (2012). https://doi.org/10.1007/s10910-012-0018-6

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  • DOI: https://doi.org/10.1007/s10910-012-0018-6

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