Weight optimization in enhanced multivariate product representation (EMPR) for given supports at the fluctuation free integration limit

Abstract

This work focuses on the weight optimization via constancy maximization using the recently proposed decomposition method called "Enhanced Multivariance Product Representation" which enables us to additively express a multivariate function in terms of the less-variate components in ascending multivariance. The components are given through the terms having exactly the same level of multivariance with the target function. So certain univariate functions we call support functions are needed to keep the multivariance at the same level from term to term. The main goal is to maximize the constancy of this expansion for a given support function set with respect to the weight function of the representation. The integrations are performed by using recently conjectured and proven fluctuationlessness theorem to get rather approximate but sufficiently precise numerical values.