Univariate Function Evaluation via Contour Integration in Tridiagonal Enhanced Multivariance Products Representation (TKEMPR) Perspective: Focusing on High Oscillations<bold> </bold>

Abstract

The intended work uses the TKEMPR method which decomposes a linear integral operator on univariate functions by using high dimensional modelling with the basic idea to use Enhanced Multivariance Products Representation (EMPR) technique created and conjectured by Demiralp. The representation used here is not based on the general EMPR and is a specific EMPR construction for bivariate function decomposition. We call this decomposition Tridiagonal Kernel Enhanced Multivariance Products Representation (TKEMPR). It uses EMPR bivariate function decomposition consecutively such that in each step the remainder term is expanded to again a bivariate EMPR but with different support functions. To make a function approximation using TKEMPR, first we represent our function in terms of contour integration, then following a procedure which allows us to obtain the kernel to be used in TKEMPR, we obtain a two variable form and finally use it to approximate our function.<bold> </bold>