Open AccessOrthogonal polynomials and generalized Gauss-Rys quadrature formulae
Author(s) -
Gradimir V. Milovanović
Publication year - 2021
Publication title -
maǧallaẗ al-kuwayt li-l-ʿulūm
Language(s) - English
Resource type - Journals
eISSN - 2307-4116
pISSN - 2307-4108
DOI - 10.48129/kjs.v49i1.10665
Subject(s) - gauss–kronrod quadrature formula , gauss–jacobi quadrature , mathematics , quadrature (astronomy) , clenshaw–curtis quadrature , gaussian quadrature , orthogonal polynomials , numerical integration , gauss , gauss–laguerre quadrature , gauss–hermite quadrature , combinatorics , pure mathematics , mathematical analysis , nyström method , physics , integral equation , quantum mechanics , optics
Orthogonal polynomials and the corresponding quadrature formulas of Gaussian type concerni λ ng > the 1 e / v 2 en wei x gh > t f 0 unction ω(t; x) = exp λ (−= xt 1 2) / ( 2 1 − t2)−1/2 on (−1, 1), with parameters − and , are considered. For these quadrature rules reduce to the socalled Gauss-Rys quadrature formulas, which were investigated earlier by several authors, e.g., Dupuis at al 1976 and 1983; Sagar 1992; Schwenke 2014; Shizgal 2015; King 2016; Milovanovic ´ 2018, etc. In this generalized case, the method of modified moments is used, as well as a transformation of quadratures on (−1, 1) with N nodes to ones on (0, 1) with only (N + 1)/2 nodes. Such an approach provides a stable and very efficient numerical construction.