Computing the Coefficients for Non-Periodic Highly Oscillatory Orthonormal Functions

TL;DR

This paper develops a numerical method to compute recurrence coefficients for a basis of polynomials multiplied by sines and cosines with large fixed frequencies, aiding the analysis of highly oscillatory functions.

Contribution

It introduces a three-term recurrence relation and a numerical approach for computing its coefficients for non-periodic, highly oscillatory orthonormal functions.

Findings

Derived a three-term recurrence relation for the basis functions.

Developed a numerical method to compute recurrence coefficients.

Facilitates analysis of non-periodic highly oscillatory functions.

Abstract

A three term recurrence relation is derived for a basis consisting of polynomials multiplied by sines and cosines with large, but fixed frequencies. A numerical method for computing the coefficients of the three term recurrence relation is derived.