Computation of Gauss-type quadrature formulas with some preassigned nodes

  1. Adhemar Bultheel 1
  2. Ruymán Cruz Barroso 2
  3. Pablo González Vera 2
  4. Francisco José Perdomo Pío 2
  1. 1 K.U.Leuven
  2. 2 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

Journal:
Jaen journal on approximation

ISSN: 1889-3066

Year of publication: 2010

Volume: 2

Issue: 2

Pages: 163-191

Type: Article

Abstract

When dealing with the approximate calculation of weighted integrals over a finite interval [a, b], Gauss-type quadrature rules with one or two prescribed nodes at the end points {a, b} are well known and commonly referred as Gauss-Radau and Gauss-Lobatto formulas respectively. In this regard, efficient algorithms involving the solution of an eigenvalue problem for certain tri-diagonal (Jacobi) matrices are available for their computation. In this work a further step will be given by adding to the above quadratures an extra fixed node in (a, b) and providing similar efficient algorithms for their computation. This will be done by passing to the unit circle and taking advantage of the so-called Szeg˝o-Lobatto quadrature rules recently introduced in [27] and [6].