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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
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     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 },
     year = {2018},
     volume = {43},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2018_43_a4/}
}
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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/