On the convergence

of certain Gauss-type quadrature formulas

for unbounded intervals

Authors:
A. Bultheel, C. Díaz-Mendoza, P. González-Vera and R. Orive

Journal:
Math. Comp. **69** (2000), 721-747

MSC (1991):
Primary 65D30; Secondary 41A21

DOI:
https://doi.org/10.1090/S0025-5718-99-01107-2

Published electronically:
February 24, 1999

MathSciNet review:
1651743

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the convergence of Gauss-type quadrature formulas for the integral , where is a weight function on the half line . The -point Gauss-type quadrature formulas are constructed such that they are exact in the set of Laurent polynomials }, where is a sequence of integers satisfying and . It is proved that under certain Carleman-type conditions for the weight and when or goes to , then convergence holds for all functions for which is integrable on . Some numerical experiments compare the convergence of these quadrature formulas with the convergence of the classical Gauss quadrature formulas for the half line.

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Additional Information

**A. Bultheel**

Affiliation:
Department of Computer Science, K.U. Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium

Email:
Adhemar.Bultheel@cs.kuleuven.ac.be

**C. Díaz-Mendoza**

Affiliation:
Department Mathematical Analysis, Univ. La Laguna, Tenerife, Canary Islands, Spain

Email:
cjdiaz@ull.es

**P. González-Vera**

Affiliation:
Department Mathematical Analysis, Univ. La Laguna, Tenerife, Canary Islands, Spain

Email:
pglez@ull.es

**R. Orive**

Affiliation:
Department Mathematical Analysis, Univ. La Laguna, Tenerife, Canary Islands, Spain

Email:
rorive@ull.es

DOI:
https://doi.org/10.1090/S0025-5718-99-01107-2

Received by editor(s):
March 3, 1998

Received by editor(s) in revised form:
May 19, 1998

Published electronically:
February 24, 1999

Additional Notes:
The work of the first author is partially supported by the Fund for Scientific Research (FWO), project “Orthogonal systems and their applications”, grant #G.0278.97, and the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Minister’s Office for Science, Technology and Culture. The scientific responsibility rests with the author.

The work of the other three authors was partially supported by the scientific research project PB96-1029 of the Spanish D.G.I.C.Y.T

Dedicated:
Dedicated to Professor Nácere Hayek Calil on the occasion of his 75th birthday

Article copyright:
© Copyright 2000
American Mathematical Society