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A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations | Advances in Computational Mathematics Skip to main content
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A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations

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Abstract

We describe the parallelisation of the GMRES(c) algorithm and its implementation on distributed-memory architectures, using both networks of transputers and networks of workstations under the PVM message-passing system. The test systems of linear equations considered are those derived from five-point finite-difference discretisations of partial differential equations. A theoretical model of the computation and communication phases is presented which allows us to decide for which values of the parameterc our implementation executes efficiently. The results show that for reasonably large discretisation grids the implementations are effective on a large number of processors.

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Authors and Affiliations

  1. Centro de Processamento de Dados, Universidade Federal do Rio Grande do Sul, Brazil

    Rudnei Dias da Cunha

  2. Computing Laboratory, University of Kent, Canterbury, UK

    Rudnei Dias da Cunha

  3. Computing Laboratory, University of Kent, Canterbury, UK

    Tim Hopkins

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  1. Rudnei Dias da Cunha
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  2. Tim Hopkins
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da Cunha, R.D., Hopkins, T. A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations. Adv Comput Math 2, 261–277 (1994). https://doi.org/10.1007/BF02521112

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  • DOI: https://doi.org/10.1007/BF02521112

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