Enhanced Multivariate Product Representation Applied to the Remainder Term of a Multivariate Taylor Expansion Expressed as a Cauchy Integral Form

摘要

Enhanced Multivariate Product Representation (EMPR) provides a better approximation for multivariate functions just by using less expansion terms compared to High Dimensional Model Representation (HDMR). This is done via so called support functions. Fluctuationlessness theorem provides us with a good approximation of integrated expressions under certain conditions. Taking a Taylor expansion of a multivariate function with the remainder term written in integral form and transforming the remainder part to a cauchy contour integral followed by the application of EMPR over the variables and if necessary calculating the support functions via fluctuationlessness takes us to better approximations of multivariate functions.