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Symbolic–numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal B-spline

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Abstract

The first 60 coefficients in the three-term recurrence relation for monic polynomials orthogonal with respect to cardinal B-splines φ m as the weight functions on [0, m] (m ∈ ℕ) are obtained in a symbolic form. They enable calculation of parameters, nodes, and weights, in the corresponding Gaussian quadrature up to 60 nodes. The efficiency of these Gaussian quadratures is shown in some numerical examples. Finally, two interesting conjectures are stated.

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Authors and Affiliations

  1. Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

  2. State University of Novi Pazar, Novi Pazar, Serbia

    Gradimir V. Milovanović

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  1. Gradimir V. Milovanović
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Correspondence to Gradimir V. Milovanović.

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Dedicated to Prof. Walter Gautschi on the occasion of his 90th birthday

The author was supported in part by the Serbian Ministry of Education, Science and Technological Development (No. #OI 174015).

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Milovanović, G.V. Symbolic–numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal B-spline. Numer Algor 76, 333–347 (2017). https://doi.org/10.1007/s11075-016-0256-y

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  • DOI: https://doi.org/10.1007/s11075-016-0256-y

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