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International Conference on High-Performance Computing and Networking

HPCN-Europe 1997: High-Performance Computing and Networking pp 389–399Cite as

The improved quasi-minimal residual method on massively distributed memory computers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1225))

Abstract

For the solutions of linear systems of equations with unsymmetric coefficient matrices, we propose an improved version of the quasi-minimal residual (IQMR) method by using the Lanczos process as a major component combining elements of numerical stability and parallel algorithm design. For Lanczos process, stability is obtained by a coupled two-term procedure that generates Lanczos vectors normalized to unit length. The algorithm is derived in such a way that all inner products and matrix-vector multiplications of a single iteration step are independent, subsequently communication time required for inner products can be overlapped efficiently with computation time. Therefore, the cost of global communication on parallel distributed memory computers is significantly reduced. The resulting IQMR algorithm preserves the favorable properties of the Lanczos process without increasing computational costs. The efficiency of this method is demonstrated by numerical experimental results carried out on a massively parallel distributed memory computer, the Parsytec GC/PowerPlus.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Linköping University, S-581 83, Linköping, Sweden

    Tian-Ruo Yang

  2. Department of Technical Mathematics and Computer Science, TU Delft, P.O. Box 356, 2600, AJ Delft, The Netherlands

    Hai-Xiang Lin

Authors
  1. Tian-Ruo Yang
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  2. Hai-Xiang Lin
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Bob Hertzberger Peter Sloot

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© 1997 Springer-Verlag Berlin Heidelberg

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Yang, TR., Lin, HX. (1997). The improved quasi-minimal residual method on massively distributed memory computers. In: Hertzberger, B., Sloot, P. (eds) High-Performance Computing and Networking. HPCN-Europe 1997. Lecture Notes in Computer Science, vol 1225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031611

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  • DOI: https://doi.org/10.1007/BFb0031611

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62898-9

  • Online ISBN: 978-3-540-69041-2

  • eBook Packages: Springer Book Archive

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