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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On generalized averaged Gaussian formulas
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by Miodrag M. Spalević PDF
Math. Comp. 76 (2007), 1483-1492 Request permission

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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Additional Information
  • Miodrag M. Spalević
  • Affiliation: Department of Mathematics and Informatics, University of Kragujevac, Faculty of Science, P.O. Box 60, 34000 Kragujevac, Serbia
  • MR Author ID: 600543
  • Email: spale@kg.ac.yu
  • Received by editor(s): August 9, 2005
  • Received by editor(s) in revised form: May 4, 2006
  • Published electronically: 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 2007 American Mathematical Society
  • Journal: Math. Comp. 76 (2007), 1483-1492
  • MSC (2000): Primary 65D30, 65D32; Secondary 33A65
  • DOI: https://doi.org/10.1090/S0025-5718-07-01975-8
  • MathSciNet review: 2299784