Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness |
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| Authors: | Gradimir V. Milovanović Aleksandar S. Cvetković Marija P. Stanić |
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| Affiliation: | (1) Faculty of Computer Sciences, Megatrend University, Bulevar Umetnosti 29, 11070 Novi Beograd, Serbia;(2) Department of Mathematics and Informatics, Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000 Nis, Serbia;(3) Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovića 12, 34000 Kragujevac, Serbia |
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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. 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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| Keywords: | KeywordHeading" >Mathematics Subject Classification (2000) 65D30 65D32 42A05 |
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