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Quadrature Rules with Multiple Nodes

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Mathematical Analysis, Approximation Theory and Their Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 111))

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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Acknowledgements

The authors were supported in part by the Serbian Ministry of Education, Science and Technological Development (grant number #174015).

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Authors and Affiliations

  1. The Serbian Academy of Sciences and Arts, Kneza Mihaila 35, 11000, Belgrade, Serbia

    Gradimir V. Milovanović

  2. Faculty of Science, Department of Mathematics and Informatics, University of Kragujevac, Radoja Domanovića 12, 34000, Kragujevac, Serbia

    Marija P. Stanić

Authors
  1. Gradimir V. Milovanović
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  2. Marija P. Stanić
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Correspondence to Gradimir V. Milovanović .

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Editors and Affiliations

  1. Department of Mathematics, National Technical Unversity of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Mathematics, Netaji Subhas Instit. of Tech., New Delhi, India

    Vijay Gupta

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Milovanović, G.V., Stanić, M.P. (2016). Quadrature Rules with Multiple Nodes. In: Rassias, T., Gupta, V. (eds) Mathematical Analysis, Approximation Theory and Their Applications. Springer Optimization and Its Applications, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-31281-1_19

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