DAIS - Digital Archive of the Serbian Academy of Sciences and Arts
    • English
    • Српски
    • Српски (Serbia)
  • English 
    • English
    • Serbian (Cyrillic)
    • Serbian (Latin)
  • Login
View Item 
  •   DAIS
  • Cрпска академија наука и уметности / Serbian Academy of Sciences and Arts
  • Bulletin
  • Classe des sciences mathematiques et naturelles
  • View Item
  •   DAIS
  • Cрпска академија наука и уметности / Serbian Academy of Sciences and Arts
  • Bulletin
  • Classe des sciences mathematiques et naturelles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

An efficient computation of parameters in the Rys quadrature formula

Thumbnail
2018
Milovanovic.pdf (495.8Kb)
Authors
Milovanović, Gradimir V.
Conference object (Published version)
Metadata
Show full item record
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 polynomials
Source:
Bulletin T.CLI de l’Académie serbe des sciences et des arts, 2018, 39-64
Publisher:
  • 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)

ISSN: 0561-7332

[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_dais_9083
URI
https://dais.sanu.ac.rs/123456789/9083
Collections
  • Classe des sciences mathematiques et naturelles
Institution/Community
Cрпска академија наука и уметности / Serbian Academy of Sciences and Arts
TY  - 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 .

DSpace software copyright © 2002-2015  DuraSpace
About DAIS - Digital Archive of the Serbian Academy of Sciences and Arts | Send Feedback

CoreTrustSealre3dataOpenAIRERCUB
 

 

All of DSpaceInstitutions/communitiesAuthorsTitlesSubjectsThis institutionAuthorsTitlesSubjects

Statistics

View Usage Statistics

DSpace software copyright © 2002-2015  DuraSpace
About DAIS - Digital Archive of the Serbian Academy of Sciences and Arts | Send Feedback

CoreTrustSealre3dataOpenAIRERCUB