Mathematics of Computation

Author(s): Miodrag M. Spalevic.
Journal: Math. Comp. 76 (2007), 1483-1492.
MSC (2000): Primary 65D30, 65D32; Secondary 33A65.
Posted: March 8, 2007
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Abstract: We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions $w(x)\equiv w^{(\alpha,\beta)}(x)=(1-x)^\alpha(1+x)^\beta$ ( $\alpha,\beta>-1$ ) we give a necessary and sufficient condition on the parameters $\alpha$ and $\beta$ such that the optimal averaged Gaussian quadrature formulas are internal.

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Retrieve articles in Mathematics of Computation with MSC (2000): 65D30, 65D32, 33A65.

Miodrag M. Spalevic
Affiliation: Department of Mathematics and Informatics, University of Kragujevac, Faculty of Science, P.O. Box 60, 34000 Kragujevac, Serbia
Email: spale@kg.ac.yu

DOI: 10.1090/S0025-5718-07-01975-8
PII: S 0025-5718(07)01975-8
Keywords: Averaged and anti-Gaussian quadrature formula, optimal stratified extension, three-term recurrence relation, positive quadrature formula, Gauss, Jacobi matrix, Kronrod
Received by editor(s): August 9, 2005 and in revised form, May 4, 2006
Posted: March 8, 2007
Additional Notes: The author was supported in part by the Serbian Ministry of Science and Environmental Protection (Project #144005A: ``Approximation of linear operators'').
Copyright of article: Copyright 2007, American Mathematical Society

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