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 |
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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 journal › Article
}
TY - JOUR
T1 - Numerical integration using rys polynomials
AU - King, Harry F.
AU - Dupuis, Michel
PY - 1976
Y1 - 1976
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0001142721&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0001142721&partnerID=8YFLogxK
U2 - 10.1016/0021-9991(76)90008-5
DO - 10.1016/0021-9991(76)90008-5
M3 - Article
AN - SCOPUS:0001142721
VL - 21
SP - 144
EP - 165
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
IS - 2
ER -