Affine transformational enhanced multivariance product representation (ATEMPR) and its relation to rational approximants

This work focuses on the development of a univariate function approximating method by using recently proposed extension to high dimensional model representation, enhanced multivariance product representation (EMPR). The method uses the target function's image under an affine transformation for EMPR instead of the function's itself. The affine transformation is a first degree polynomial in the target function with coefficients depending on the independent variable operator. These coefficients are taken as certain degree polynomials in the independent variable operator whose coefficients are to be determined by maximizing the constancy measurer of the EMPR for the image of the function under this transformation. The resulting scheme is in a rational function structure. The fundamentally conceptual and constructional issues are given here. The illustrative implementations will be given in the presentation and in the journal publication.