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Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab

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Abstract

In this paper, we investigate variants of the well-known Golub and Welsch algorithm for computing nodes and weights of Gaussian quadrature rules for symmetric weights w in intervals (−a, a) (not necessarily bounded). The purpose is to reduce the complexity of the Jacobi eigenvalue problem stemming from Wilf’s theorem and show the effectiveness of Matlab implementations of our variants for reducing the computer times compared to some other methods. Numerical examples on three test problems show the benefits of these variants.

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Authors and Affiliations

  1. 30 rue du sergent Bauchat, 75012, Paris, France

    Gérard Meurant

  2. University of Padua, Padua, Italy

    Alvise Sommariva

Authors
  1. Gérard Meurant
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  2. Alvise Sommariva
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Correspondence to Alvise Sommariva.

Additional information

Work supported by the “ex-60%” funds and by the project “Interpolation and Extrapolation: new algorithms and applications” of the University of Padova, and by the INdAM GNCS.

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Meurant, G., Sommariva, A. Fast variants of the Golub and Welsch algorithm for symmetric weight functions in Matlab. Numer Algor 67, 491–506 (2014). https://doi.org/10.1007/s11075-013-9804-x

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  • DOI: https://doi.org/10.1007/s11075-013-9804-x

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