Fluctuation free multivariate integration based logarithmic HDMR in multivariate function representation |
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Authors: | Burcu Tunga Metin Demiralp |
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Institution: | (1) Informatics Institute, Istanbul Technical University, 34469 Besiktas, Istanbul, Turkey |
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Abstract: | This paper focuses on the Logarithmic High Dimensional Model Representation (Logarithmic HDMR) method which is a divide–and–conquer
algorithm developed for multivariate function representation in terms of less-variate functions to reduce both the mathematical
and the computational complexities. The main purpose of this work is to bypass the evaluation of N–tuple integrations appearing in Logarithmic HDMR by using the features of a new theorem named as Fluctuationlessness Approximation
Theorem. This theorem can be used to evaluate the complicated integral structures of any scientific problem whose values can
not be easily obtained analytically and it brings an approximation to the values of these integrals with the help of the matrix
representation of functions. The Fluctuation Free Multivariate Integration Based Logarithmic HDMR method gives us the ability
of reducing the complexity of the scientific problems of chemistry, physics, mathematics and engineering. A number of numerical
implementations are also given at the end of the paper to show the performance of this new method. |
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Keywords: | |
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