An efficient computation of parameters in the Rys quadrature formula
Abstract
We present an efficient procedure for constructing the so-called Gauss-Rys
quadrature formulas and the corresponding polynomials orthogonal on (−1, 1) with respect
to the even weight function w(t; x) = exp(−xt2), where x a positive parameter. Such GaussRys quadrature formulas were investigated earlier e.g. by M. Dupuis, J. Rys, H.F. King [J.
Chem. Phys. 65 (1976), 111 − 116; J. Comput. Chem. 4 (1983), 154 − 157], D.W. Schwenke
[Comput. Phys. Comm. 185 (2014), 762 − 763], and B.D. Shizgal [Comput. Theor. Chem.
1074 (2015), 178 − 184], and were used to evaluate electron repulsion integrals in quantum chemistry computer codes. The approach in this paper is based to a transformation of
quadratures on (−1, 1) with N nodes to ones on (0, 1) with only [(N + 1)/2] nodes and their
construction. The method of modified moments is used for getting recurrence coefficients.
Numerical experiments are included.
Keywords:
numerical integration / Gaussian quadrature / orthogonal polynomialsSource:
Bulletin T.CLI de l’Académie serbe des sciences et des arts, 2018, 39-64Publisher:
- Beograd : Académie Serbe des sciences et des arts
Funding / projects:
- Approximation of integral and differential operators and applications (RS-174015)
- Serbian Academy of Sciences and Arts, Project F-96
Note:
- Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles. Sciences mathématiques. - 43, 151 (2018)
Collections
Institution/Community
Cрпска академија наука и уметности / Serbian Academy of Sciences and ArtsTY - CONF AU - Milovanović, Gradimir V. PY - 2018 UR - https://dais.sanu.ac.rs/123456789/9083 AB - We present an efficient procedure for constructing the so-called Gauss-Rys quadrature formulas and the corresponding polynomials orthogonal on (−1, 1) with respect to the even weight function w(t; x) = exp(−xt2), where x a positive parameter. Such GaussRys quadrature formulas were investigated earlier e.g. by M. Dupuis, J. Rys, H.F. King [J. Chem. Phys. 65 (1976), 111 − 116; J. Comput. Chem. 4 (1983), 154 − 157], D.W. Schwenke [Comput. Phys. Comm. 185 (2014), 762 − 763], and B.D. Shizgal [Comput. Theor. Chem. 1074 (2015), 178 − 184], and were used to evaluate electron repulsion integrals in quantum chemistry computer codes. The approach in this paper is based to a transformation of quadratures on (−1, 1) with N nodes to ones on (0, 1) with only [(N + 1)/2] nodes and their construction. The method of modified moments is used for getting recurrence coefficients. Numerical experiments are included. PB - Beograd : Académie Serbe des sciences et des arts C3 - Bulletin T.CLI de l’Académie serbe des sciences et des arts T1 - An efficient computation of parameters in the Rys quadrature formula SP - 39 EP - 64 UR - https://hdl.handle.net/21.15107/rcub_dais_9083 ER -
@conference{ author = "Milovanović, Gradimir V.", year = "2018", abstract = "We present an efficient procedure for constructing the so-called Gauss-Rys quadrature formulas and the corresponding polynomials orthogonal on (−1, 1) with respect to the even weight function w(t; x) = exp(−xt2), where x a positive parameter. Such GaussRys quadrature formulas were investigated earlier e.g. by M. Dupuis, J. Rys, H.F. King [J. Chem. Phys. 65 (1976), 111 − 116; J. Comput. Chem. 4 (1983), 154 − 157], D.W. Schwenke [Comput. Phys. Comm. 185 (2014), 762 − 763], and B.D. Shizgal [Comput. Theor. Chem. 1074 (2015), 178 − 184], and were used to evaluate electron repulsion integrals in quantum chemistry computer codes. The approach in this paper is based to a transformation of quadratures on (−1, 1) with N nodes to ones on (0, 1) with only [(N + 1)/2] nodes and their construction. The method of modified moments is used for getting recurrence coefficients. Numerical experiments are included.", publisher = "Beograd : Académie Serbe des sciences et des arts", journal = "Bulletin T.CLI de l’Académie serbe des sciences et des arts", title = "An efficient computation of parameters in the Rys quadrature formula", pages = "39-64", url = "https://hdl.handle.net/21.15107/rcub_dais_9083" }
Milovanović, G. V.. (2018). An efficient computation of parameters in the Rys quadrature formula. in Bulletin T.CLI de l’Académie serbe des sciences et des arts Beograd : Académie Serbe des sciences et des arts., 39-64. https://hdl.handle.net/21.15107/rcub_dais_9083
Milovanović GV. An efficient computation of parameters in the Rys quadrature formula. in Bulletin T.CLI de l’Académie serbe des sciences et des arts. 2018;:39-64. https://hdl.handle.net/21.15107/rcub_dais_9083 .
Milovanović, Gradimir V., "An efficient computation of parameters in the Rys quadrature formula" in Bulletin T.CLI de l’Académie serbe des sciences et des arts (2018):39-64, https://hdl.handle.net/21.15107/rcub_dais_9083 .