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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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A homographic best approximation problem with application to optimized Schwarz waveform relaxation
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by D. Bennequin, M. J. Gander and L. Halpern PDF
Math. Comp. 78 (2009), 185-223 Request permission

Abstract:

We present and study a homographic best approximation problem, which arises in the analysis of waveform relaxation algorithms with optimized transmission conditions. Its solution characterizes in each class of transmission conditions the one with the best performance of the associated waveform relaxation algorithm. We present the particular class of first order transmission conditions in detail and show that the new waveform relaxation algorithms are well posed and converge much faster than the classical one: the number of iterations to reach a certain accuracy can be orders of magnitudes smaller. We illustrate our analysis with numerical experiments.
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Additional Information
  • D. Bennequin
  • Affiliation: Institut de Mathématiques de Jussieu, Université Paris VII, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France
  • Email: bennequin@math.jussieu.fr
  • M. J. Gander
  • Affiliation: Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, CP 240, CH-1211 Genève, Switzerland
  • Email: Martin.Gander@math.unige.ch
  • L. Halpern
  • Affiliation: LAGA,Institut Galilée, Université Paris XIII, 93430 Villetaneuse, France
  • Email: halpern@math.univ-paris13.fr
  • Received by editor(s): November 14, 2006
  • Received by editor(s) in revised form: December 1, 2007
  • Published electronically: August 4, 2008
  • © Copyright 2008 American Mathematical Society
  • Journal: Math. Comp. 78 (2009), 185-223
  • MSC (2000): Primary 65M12, 65M55, 30E10
  • DOI: https://doi.org/10.1090/S0025-5718-08-02145-5
  • MathSciNet review: 2448703