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Topics in Numerical Analysis pp 91–104Cite as

On Linear Asynchronous Iterations when the Spectral Radius of the Modulus Matrix is One

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Part of the book series: Computing Supplementa ((COMPUTING,volume 15))

Abstract

A classical result on linear asynchronous iterations states that convergence occurs if and only if the spectral radius of the modulus matrix is less than 1. The present paper shows that if one introduces very mild restrictions on the admissible asynchronous processes, one gets convergence for a larger class of matrices for which the spectral radius of the modulus matrix is allowed to be equal to 1. The mild restrictions are virtually always fulfilled in practical implementations. In this manner, our result contributes to the better understanding of the different hypotheses underlying mathematical models for asynchronous iterations.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Wuppertal, D-42097, Wuppertal, Germany

    A. Frommer

  2. ENSEEIHT: Ecole Nationale Supérieure d’Electrotechnique, d’Electronique, d’Informatique et d’Hydraulique de Toulouse, 2, rue Camichel, B.P. 7122, F-31071, Toulouse-Cédex 1, France

    P. Spiteri

Authors
  1. A. Frommer
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  2. P. Spiteri
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Editor information

Editors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

    Goetz Alefeld

  2. Department of Mathematical Sciences, Shimane University, Matsue, Japan

    Xiaojun Chen

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© 2001 Springer-Verlag Wien

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Frommer, A., Spiteri, P. (2001). On Linear Asynchronous Iterations when the Spectral Radius of the Modulus Matrix is One. In: Alefeld, G., Chen, X. (eds) Topics in Numerical Analysis. Computing Supplementa, vol 15. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6217-0_8

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  • DOI: https://doi.org/10.1007/978-3-7091-6217-0_8

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83673-6

  • Online ISBN: 978-3-7091-6217-0

  • eBook Packages: Springer Book Archive

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