Volume 45, pp. 476-498, 2016.

Weighted Hermite quadrature rules

Mohammad Masjed-Jamei and Gradimir V. Milovanović


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

ETNA articles which cite this article

Vol. 52 (2020), pp. 113-131 Jiayin Zhai, Zhiyue Zhang, and Tongke Wang: Fractional Hermite interpolation for non-smooth functions

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