Journal of Mathematical Chemistry

, Volume 49, Issue 4, pp 894–909 | Cite as

Fluctuation free multivariate integration based logarithmic HDMR in multivariate function representation

  • Burcu Tunga
  • Metin Demiralp
Original Paper


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.


High dimensional model representation Multivariate functions Approximation 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Informatics Institute, Computational Science and Engineering Program, Group for Science and Methods of Computation Maslakİstanbul Technical UniversityİstanbulTurkey

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