Szegö quadrature formulas for certain Jacobi-type weight functions

Authors:
Leyla Daruis, Pablo González-Vera and Olav Njåstad

Journal:
Math. Comp. **71** (2002), 683-701

MSC (2000):
Primary 41A55, 33C45

DOI:
https://doi.org/10.1090/S0025-5718-01-01337-0

Published electronically:
October 4, 2001

MathSciNet review:
1885621

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we are concerned with the estimation of integrals on the unit circle of the form by means of the so-called Szegö quadrature formulas, i.e., formulas of the type with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions related to the Jacobi functions for the interval nodes and weights in Szegö quadrature formulas are explicitly deduced. Illustrative numerical examples are also given.

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Additional Information

**Leyla Daruis**

Affiliation:
Department of Mathematical Analysis, La Laguna University, Tenerife, Canary Islands, Spain

Email:
ldaruis@ull.es

**Pablo González-Vera**

Affiliation:
Corresponding author: Department of Mathematical Analysis, La Laguna University, 38271- La Laguna, Tenerife, Spain

Email:
pglez@ull.es. Fax: 34-922-318195

**Olav Njåstad**

Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

Email:
njastad@math.ntnu.no

DOI:
https://doi.org/10.1090/S0025-5718-01-01337-0

Keywords:
Weight functions,
quadrature formulas,
orthogonal polynomials,
Szeg\"o polynomials,
error bounds

Received by editor(s):
February 11, 2000

Received by editor(s) in revised form:
July 10, 2000

Published electronically:
October 4, 2001

Additional Notes:
The work of the first author was performed as part of a grant of the Gobierno de Canarias.

The work of the second author was supported by the Scientific Research Project of the Spanish D.G.E.S. under contract PB96-1029.

Article copyright:
© Copyright 2001
American Mathematical Society