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Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness

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Abstract

In this paper we consider interpolatory quadrature formulae with multiple nodes, which have the maximal trigonometric degree of exactness. Our approach is based on a procedure given by Ghizzeti and Ossicini (Quadrature formulae, Academie-Verlag, Berlin, 1970). We introduce and consider the so-called σ-orthogonal trigonometric polynomials of semi-integer degree and give a numerical method for their construction. Also, some numerical examples are included.

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Authors and Affiliations

  1. Faculty of Computer Sciences, Megatrend University, Bulevar Umetnosti 29, 11070, Novi Beograd, Serbia

    Gradimir V. Milovanović

  2. Department of Mathematics and Informatics, Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000, Nis, Serbia

    Aleksandar S. Cvetković

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

    Marija P. Stanić

Authors
  1. Gradimir V. Milovanović
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  2. Aleksandar S. Cvetković
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  3. Marija P. Stanić
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Correspondence to Gradimir V. Milovanović.

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The authors were supported in part by the Serbian Ministry of Science and Technological Development (Project: Orthogonal Systems and Applications, grant number #144004) and the Swiss National Science Foundation (SCOPES Joint Research Project No. IB7320-111079 “New Methods for Quadrature”).

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Milovanović, G.V., Cvetković, A.S. & Stanić, M.P. Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness. Numer. Math. 112, 425–448 (2009). https://doi.org/10.1007/s00211-009-0219-5

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  • DOI: https://doi.org/10.1007/s00211-009-0219-5

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