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 language | English |
|---|---|
| Pages (from-to) | 144-165 |
| Number of pages | 22 |
| Journal | Journal of Computational Physics |
| Volume | 21 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1976 |
ASJC Scopus subject areas
- Computer Science Applications
- Physics and Astronomy(all)
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Cite this
King, H. F., & Dupuis, M. (1976). Numerical integration using rys polynomials. Journal of Computational Physics, 21(2), 144-165. https://doi.org/10.1016/0021-9991(76)90008-5