Geodesic
An efficient computation of parameters in the RYS quadrature formula
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 43 (2018), p. 39 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 $w(t;x)=\exp(-x t^2)$, where $x$ a positive parameter. Such Gauss-Rys quadrature formulas were investigated earlier e.g. by M. Dupuis, J. Rys, H.F. King $[$J. Chem. Phys. {\bf65} $(1976)$, $111-116$; J. Comput. Chem. {\bf4} $(1983)$, $154-157$]$, D.W. Schwenke $[$Comput. Phys. Comm. {\bf185} $(2014)$, $762-763$]$, and B.D. Shizgal $[$Comput. Theor. Chem.\ {\bf 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.
Classification : 41A55, 65D30, 65D32, 33C45
Keywords: numerical integration, Gaussian quadrature, orthogonal polynomials 
@article{BASS_2018_43_a4,
     author = {Gradimir V. Milovanovi\'c},
     title = {An efficient computation of parameters in the {RYS} quadrature formula},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {39 },
     publisher = {mathdoc},
     volume = {43},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2018_43_a4/}
}
TY  - JOUR
AU  - Gradimir V. Milovanović
TI  - An efficient computation of parameters in the RYS quadrature formula
JO  - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY  - 2018
SP  - 39 
VL  - 43
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASS_2018_43_a4/
LA  - en
ID  - BASS_2018_43_a4
ER  - 
%0 Journal Article
%A Gradimir V. Milovanović
%T An efficient computation of parameters in the RYS quadrature formula
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2018
%P 39 
%V 43
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASS_2018_43_a4/
%G en
%F BASS_2018_43_a4
Gradimir V. Milovanović. An efficient computation of parameters in the RYS quadrature formula. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 43 (2018), p. 39 . http://geodesic.mathdoc.fr/item/BASS_2018_43_a4/