A novel piecewise multivariate function approximation method via universal matrix representation

Süha Tuna, Burcu Tunga*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1784-1801
Number of pages18
JournalJournal of Mathematical Chemistry
Volume51
Issue number7
DOIs
Publication statusPublished - Aug 2013

Keywords

  • Approximation
  • EMPR
  • Matrix representation
  • Multidimensional problems
  • Numerical integration
  • Piecewise functions

Fingerprint

Dive into the research topics of 'A novel piecewise multivariate function approximation method via universal matrix representation'. Together they form a unique fingerprint.

Cite this