Function flattening transformational high dimensional model representation

Abstract

One of the recently developed versions of High Dimensional Model Representation (HDMR) has been used to develop certain approximation schemes for univariate and multivariate functions. The resulting approaches have been proven to be superior to some existing methods like Padé approximants, Hermite Padé approximants, and, some other branching point considering approaches have also been developed to get more efficiency in numerical applications. These use not the target function's itself but its image under certain transformations whose certain flexibilities can be optimized to get maximum constancy. Here we focus on the rather simple type transformation based Tranformational HDMR (THDMR) without introducing any kind of flexibility. Instead, we choose particular transformations such that the image of the target function to be approximated by HDMR truncations becomes sufficiently flat around a reference point. This increases the constancy of the considered THDMR. Paper has been constructed to give sufficient informations and enthusiasm around these points although it is somehow at the beginning age.