Towards Multivariate Support Function Utilization in Enhanced Multivariance Products Representation (EMPR)

摘要

Enhanced Multivariance Products Representation (EMPR) has been developed completely in Demiralp's group. It is based on High Dimensional Model Representation (HDMR) proposed by Sobol and developed by especially Rabitz and Demiralp groups even though now there are some other scientists dealing with the issue. EMPR is a somehow generalized version of HDMR by introducing univariate so-called support functions. This work is a preliminary attempt to take the issue beyond univariance by using certain multivariate support functions. Here we focus on the simplest multivariate case, bivariate EMPR and certain important issues are discussed within an appropriately detailed scheme. The basic issue is the formalism. The technical issues will be foci of the future works.