Numerical integration using rys polynomials

Harry F. King, Michel Dupuis

Research output: Contribution to journalArticle

207 Citations (Scopus)

Abstract

We define and discuss the properties of manifolds of polynomials Jn(t, x) and Rn(t, x), called Rys polynomials, which are orthonormal with respect to the weighting factor exp(-xt2) on a finite interval of t. Numerical quadrature based on Rys polynomials provides an alternative approach to the computation of integrals commonly encountered in molecular quantum mechanics. This gives rise to a curve fitting problem for the roots and quadrature weights as a function of the x parameter. We have used Chebyshev approximation for small x and an asymptotic expansion for large x. A modified Christoffel-Darboux equation applicable to Rys polynomials is derived and used to obtain alternative formulas for Rys quadrature weight factors.

Original languageEnglish
Pages (from-to)144-165
Number of pages22
JournalJournal of Computational Physics
Volume21
Issue number2
DOIs
Publication statusPublished - 1976

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numerical integration
polynomials
quadratures
Polynomials
Chebyshev approximation
weight (mass)
Quantum theory
curve fitting
Curve fitting
quantum mechanics
intervals
expansion

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Numerical integration using rys polynomials. / King, Harry F.; Dupuis, Michel.

In: Journal of Computational Physics, Vol. 21, No. 2, 1976, p. 144-165.

Research output: Contribution to journalArticle

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