Journal of Mathematical Chemistry

, Volume 51, Issue 7, pp 1784–1801 | Cite as

A novel piecewise multivariate function approximation method via universal matrix representation

  • Süha Tuna
  • Burcu Tunga
Original Paper


Multivariance in science and engineering causes problematic situations even for continous and discrete cases. One way to overcome this situation is to decrease the multivariance level of the problem by using a divide—and—conquer based method. In this sense, Enhanced Multivariance Product Representation (EMPR) plays a part in the considered scenario and acts successfully. This method brings up a finite expansion to represent a multivariate function in terms of less-variate functions with the assistance of univariate support functions. This work aims to propose a new EMPR based algorithm which has two new features that improves the determination process of each expansion component through Fluctuation Free Integration method, which is an efficient method in evaluating multiple integrals through a universal matrix representation, and increases the approximation quality through inserting a piecewise structure into the standard EMPR algorithm. This new method is called Fluctuation Free Integration based piecewise EMPR. Some numerical implementations are also given to examine the performance of this proposed method.


EMPR Piecewise functions Multidimensional problems  Approximation Matrix representation Numerical integration 

Mathematics Subject Classification (2000)

41A63 41A10 65F99 65D30 



Both authors are grateful to Prof. Demiralp for his contributions and valuable comments.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Computational Science and Engineering Program, Informatics Instituteİstanbul Technical UniversityMaslak, IstanbulTurkey
  2. 2.Department of Mathematics Engineering, Faculty of Science and Lettersİstanbul Technical UniversityMaslak, IstanbulTurkey

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