Masjed-Jamei, Mohammad; Milovanović, Gradimir V. Weighted Hermite quadrature rules. (English) Zbl 1355.65044 ETNA, Electron. Trans. Numer. Anal. 45, 476-498 (2016). Summary: In this paper, a new representation of Hermite osculatory interpolation is presented in order to construct weighted Hermite quadrature rules. Then, explicit forms of several special cases of the established quadrature are obtained such as weighted Hermite quadrature rules with arithmetic and geometric nodes as well as standard Gauss-Christoffel quadrature rules and Gaussian quadratures rules using only function derivatives. Some numerical examples are also given for the above mentioned cases. Cited in 2 Documents MSC: 65D32 Numerical quadrature and cubature formulas 41A55 Approximate quadratures 65D05 Numerical interpolation Keywords:weighted Hermite quadrature rule; Hermite interpolation; Gaussian quadrature; divided differences; distribution of nodes; Gauss-Christoffel quadrature rules; numerical examples Software:OrthogonalPolynomials PDFBibTeX XMLCite \textit{M. Masjed-Jamei} and \textit{G. V. Milovanović}, ETNA, Electron. Trans. Numer. Anal. 45, 476--498 (2016; Zbl 1355.65044) Full Text: EMIS