Experimentations on the Gaussian Wave Type Basis Set for the Matrix Representations of Certain Univariate Functions

Abstract

Recently developed Fluctuation Free Integration is based on the approximation of the function matrix representations by the images of the independent variable matrix representation under the relevant functions by using the same basis function set for both function and the independent variable. This works well as long as the integrand is a sufficiently smooth function which is analytic in a disk taking the integration domain as an interior region in the complex plane of the integration variable. This method's efficiency sensitively depends on the basis functions used in the matrix representation and therefore their behaviors throughout the integration domain. In this work we deal with the infinite interval applications by using Gaussian type basis set and aim to increase the numerical efficiency.