Fluctuation Free Matrix Representation Based Univariate Integration in Hybrid High Dimensional Model Representation (HHDMR) Over Plain and Factorized HDMR

Abstract

High Dimensional Model Representation (HDMR) which was first proposed fifteen years ago is still under development for the construction of its new varieties. It is a finite term representation of a multivariate function in terms of less variate functions. Its truncation at certain level of variance serves as an approximation to the target: function and the truncation level is preferred to be kept at most bivariance for practical applications. Plain HDMR is used for the functions highly additive while the Factorized HDMR is designed for dominantly multiplicative functions. The Hybrid HDMR (HHDMR) combines these two HDMR varieties into a new version of HDMR and is expected to work more efficiently than plain HDMR and FHDMR. The construction of HHDMR basically uses the components of plain HDMR since FHDMR does the same. The definite integrals appearing in the definition of these components are efficiently approximated by using the fluctuation free matrix representation method which was recently developed by M. Demiralp.