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Weighted Hermite quadrature rules. (English) Zbl 1355.65044

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.

MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
65D05 Numerical interpolation
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