Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules

1 March 1994

journal article
Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software

Vol. 20 (1), 21-62
https://doi.org/10.1145/174603.174605

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.

Keywords

This publication has 31 references indexed in Scilit:

A set of orthogonal polynomials induced by a given orthogonal polynomial
Aequationes mathematicae, 1993
Is the recurrence relation for orthogonal polynomials always stable?
BIT Numerical Mathematics, 1993
On the computation of generalized Fermi-Dirac and Bose-Einstein integrals
Computer Physics Communications, 1993
Quadrature formulae on half-infinite intervals
BIT Numerical Mathematics, 1991
A survey of matrix inverse eigenvalue problems
Inverse Problems, 1987
The numerical evaluation of singular integrals with coth-kernel
BIT Numerical Mathematics, 1987
Computing the Hilbert transform of a Jacobi weight function
BIT Numerical Mathematics, 1987
On the sensitivity of orthogonal polynomials to perturbations in the moments
Numerische Mathematik, 1986
Spline approximations to spherically symmetric distributions
Numerische Mathematik, 1986
Discrete approximations to spherically symmetric distributions
Numerische Mathematik, 1984

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