Algorithm xxx --- ORTHPOL: A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules

TL;DR

ORTHPOL is a comprehensive software package that provides routines for generating orthogonal polynomials, their zeros, and Gauss-type quadrature rules based on arbitrary weight functions, facilitating advanced numerical integration.

Contribution

This paper introduces a new package, ORTHPOL, offering routines for generating orthogonal polynomials and quadrature rules with arbitrary weights, along with practical examples and underlying numerical methods.

Findings

Efficient routines for computing recurrence coefficients

Accurate generation of polynomial zeros and quadrature nodes

Versatile for various weight functions

Abstract

A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the coefficients in the three-term recurrence relation satisfied by the orthogonal polynomials. Once these are known, additional data can be generated, such as zeros of orthogonal polynomials and Gauss-type quadrature rules, for which routines are also provided.