Volume 45, pp. 476-498, 2016.

Weighted Hermite quadrature rules

Mohammad Masjed-Jamei and Gradimir V. Milovanović

Abstract

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.

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Key words

weighted Hermite quadrature rule, Hermite interpolation, Gaussian quadrature, divided differences, distribution of nodes

AMS subject classifications

65D05, 65D30, 41A55, 65D32

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