Calculation of Radau–Kronrod and Lobatto–Kronrod quadrature formulas

Abstract

We show how to apply routines from the software package OPQ by Walter Gautschi in order to compute the optimal extension of an n-point generalized Radau or Lobatto formula. The method is applicable to any weight function for which enough three-term recursion coefficients are known. The idea on which the method is based was first shown by Paola Baratella in 1979. Program code in the format of M-files conforming to the conventions of OPQ is given.Keywords Quadrature formula · Optimal extension · Kronrod · ORTHPOL Computations involving orthogonal polynomialsIn a series of papers starting in 1967, gaining momentum with the survey [11] and the landmark paper [12], and culminating in the monograph [17], Walter Gautschi deeply explored the computational aspects of polynomials p k generated by three-term recursion relations of the formwith p −1 (x) = 0, p 0 (x) = 1.Dedicated to Walter Gautschi, at 79 still a pioneer.