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Efficient Biorthogonal Lanczos Algorithm on Message Passing Parallel Computer

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Methods and Tools of Parallel Programming Multicomputers (MTPP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6083))

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Abstract

Many important scientific and engineering problems require the computation of a small number of eigenvalues of large nonsymmetric matrices. The biorthogonal Lanczos method is one of the methods to solve that problem. In this paper, we introduce the s-step biorthogonal Lanczos method generating reduction matrices which are similar to reduction matrices generated by the standard biorthogonal Lanczos method. The s-step generalization of biorthogonal Lanczos method enhances parallel properties by forming s simultaneous search direction vectors. The s-step biorthogonal Lanczos method has the minimized synchronization points, which resulted in the minimized global communication compared to the standard biorthogonal Lanczos method.

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Authors and Affiliations

  1. School of Computer and Information Technology, Daegu University, Korea

    Sun Kyung Kim

Authors
  1. Sun Kyung Kim
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, Chung Hua University, 300, Hsinchu, Taiwan, China

    Ching-Hsien Hsu

  2. Supercomputer Software Department, Institute of Computational Mathematics and Mathematical Geophysics, Pr. Lavrentieva, ICM&MG RAS, 630090, Novosibirsk, Russia

    Victor Malyshkin

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Kim, S.K. (2010). Efficient Biorthogonal Lanczos Algorithm on Message Passing Parallel Computer. In: Hsu, CH., Malyshkin, V. (eds) Methods and Tools of Parallel Programming Multicomputers. MTPP 2010. Lecture Notes in Computer Science, vol 6083. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14822-4_33

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  • DOI: https://doi.org/10.1007/978-3-642-14822-4_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14821-7

  • Online ISBN: 978-3-642-14822-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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