Szegö quadrature formulas for certain Jacobitype weight functions
Authors:
Leyla Daruis, Pablo GonzálezVera and Olav Njåstad
Journal:
Math. Comp. 71 (2002), 683701
MSC (2000):
Primary 41A55, 33C45
Published electronically:
October 4, 2001
MathSciNet review:
1885621
Fulltext PDF Free Access
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Abstract: In this paper we are concerned with the estimation of integrals on the unit circle of the form by means of the socalled 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 GonzálezVera
Affiliation:
Corresponding author: Department of Mathematical Analysis, La Laguna University, 38271 La Laguna, Tenerife, Spain
Email:
pglez@ull.es. Fax: 34922318195
Olav Njåstad
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
Email:
njastad@math.ntnu.no
DOI:
http://dx.doi.org/10.1090/S0025571801013370
PII:
S 00255718(01)013370
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 PB961029.
Article copyright:
© Copyright 2001
American Mathematical Society
