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Numerical Algorithms

, Volume 67, Issue 3, pp 491–506 | Cite as

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

  • Gérard Meurant
  • Alvise Sommariva
Original Paper

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.

Keywords

Algebraic quadrature Symmetric weights Golub and Welsch algorithm 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.ParisFrance
  2. 2.University of PaduaPaduaItaly

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