Computing Gaussian quadrature rules with high relative accuracy

Laudadio, Teresa;Mastronardi, Nicola;Van Dooren, Paul
(2022) Numerical Algorithms — Vol. 92, n° 1, p. 767-793 (2022)

Files

LaudadioMV22.pdf
  • Open Access
  • Adobe PDF
  • 1.52 MB
Download

Details

Authors
  • Laudadio, TeresaIstituto per le Applicazioni del Calcolo “M. Picone”, Bari, Italy
    Author
  • Mastronardi, NicolaIstituto per le Applicazioni del Calcolo “M. Picone”, Bari, Italy
    Author
  • Van Dooren, PaulUCLouvain
    Author
Abstract
The computation of n-point Gaussian quadrature rules for symmetric weight functions is considered in this paper. It is shown that the nodes and the weights of the Gaussian quadrature rule can be retrieved from the singular value decomposition of a bidiagonal matrix of size n/2. The proposed numerical method allows to compute the nodes with high relative accuracy and a computational complexity of O(n2). We also describe an algorithm for computing the weights of a generic Gaussian quadrature rule with high relative accuracy. Numerical examples show the effectiveness of the proposed approach.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Laudadio, T., Mastronardi, N., & Van Dooren, P. (2022). Computing Gaussian quadrature rules with high relative accuracy. Numerical Algorithms, 92(1), 767-793. https://doi.org/10.1007/s11075-022-01297-9 (Original work published 2022)