Basic features of conic transformational high dimensional model representation

Abstract

The basic philosophy behind THDMR is to transform a multivariate function to another multivariate function such that the HDMR expansion of the new function is much more efficient. A previous work using affine transformation forms milestone to this work where a conic (affine plus quadratic) transformation is considered with an attempt to optimize its coefficients. Fundamental formulation has been completely based on that work although the derived formulae and the corresponding approximants in literature (Hermite - Padé) are completely different because of branch points. © 2010 American Institute of Physics.