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Published in:
A Brief History of the Favard Operator and Its Variants Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Quadrature Rules with Multiple Nodes

Authors : Gradimir V. Milovanović, Marija P. Stanić

Published in: Mathematical Analysis, Approximation Theory and Their Applications

Publisher: Springer International Publishing

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Abstract

In this paper a brief historical survey of the development of quadrature rules with multiple nodes and the maximal algebraic degree of exactness is given. The natural generalization of such rules are quadrature rules with multiple nodes and the maximal degree of exactness in some functional spaces that are different from the space of algebraic polynomial. For that purpose we present a generalized quadrature rules considered by Ghizzeti and Ossicini (Quadrature Formulae, Academie, Berlin, 1970) and apply their ideas in order to obtain quadrature rules with multiple nodes and the maximal trigonometric degree of exactness. Such quadrature rules are characterized by the so-called s- and \(\sigma\)-orthogonal trigonometric polynomials. Numerical method for constructing such quadrature rules is given, as well as a numerical example to illustrate the obtained theoretical results.

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previous chapter Localized Summability Kernels for Jacobi Expansions
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Metadata
Title
Quadrature Rules with Multiple Nodes
Authors
Gradimir V. Milovanović
Marija P. Stanić
Copyright Year
2016
Book
Mathematical Analysis, Approximation Theory and Their Applications

Print ISBN: 978-3-319-31279-8

Electronic ISBN: 978-3-319-31281-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-31281-1_19

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