Paper Info
Title
A factorized high dimensional model representation on the nodes of a finite hyperprismatic regular grid
Abstract
When the values of a multivariate function f(x\"1,...,x\"N), having N independent variables like x\"1,...,x\"N are given at the nodes of a cartesian product set in the space of the independent variables and an interpolation problem is defined to find out the analytical structure of this function some difficulties arise in the standard methods due to the multidimensionality of the problem. Here, the main purpose is to partition this multivariate data into low-variate data and to obtain the analytical structure of the multivariate function by using this partitioned data. High dimensional model representation (HDMR) is used for these types of problems. However, if HDMR requires all components, which means 2^N number of components, to get a desired accuracy then factorized high dimensional model representation (FHDMR) can be used. This method uses the components of HDMR. This representation is needed when the sought multivariate function has a multiplicative nature. In this work we introduce how to utilize FHDMR for these problems and present illustrative examples.
Year
DOI
Venue
2005
10.1016/j.amc.2004.06.056
Applied Mathematics and Computation
Keywords
Field
DocType
interpolation,multivariate functions,high dimensional model representation,approximation,multidimensional problems,cartesian product,multivariate data,analytical function,multidimensional analysis,numerical analysis,interpolacion,value function,applied mathematics
Applied mathematics,Combinatorics,Multiplicative function,Regular grid,Mathematical analysis,Cartesian product,Interpolation,Multidimensional analysis,Analytic function,Partition (number theory),High-dimensional model representation,Mathematics
Journal
Volume
Issue
ISSN
164
3
Applied Mathematics and Computation
Citations 
PageRank 
References 
5
0.78
0
Authors
2
Name
Order
Citations
PageRank
M. Alper Tunga1405.44
Metin Demiralp2335.48