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Nonstandard Gaussian quadrature formulae based on operator values

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Abstract

In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorithm for constructing such quadrature formulae. In particular, for some special classes of linear operators we obtain interesting explicit results connected with theory of orthogonal polynomials.

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Author information

Authors and Affiliations

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

    Gradimir V. Milovanović

  2. Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000, Niš, Serbia

    Aleksandar S. Cvetković

Authors
  1. Gradimir V. Milovanović
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  2. Aleksandar S. Cvetković
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Correspondence to Gradimir V. Milovanović.

Additional information

Communicated by Lothar Reichel.

The authors were supported in parts by the Serbian Ministry of Science and Technological Development (Project #144004G “Orthogonal Systems and Applications”).

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Milovanović, G.V., Cvetković, A.S. Nonstandard Gaussian quadrature formulae based on operator values. Adv Comput Math 32, 431–486 (2010). https://doi.org/10.1007/s10444-009-9114-y

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