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A Normalization Scheme for the Non-symmetric s-Step Lanczos Algorithm

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Algorithms and Architectures for Parallel Processing (ICA3PP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8286))

Abstract

The Lanczos algorithm is among the most frequently used techniques for computing a few dominant eigenvalues of a large sparse non-symmetric matrix. When variants of this algorithm are implemented on distributed-memory computers, the synchronization time spent in computing dot products is increasingly limiting the parallel scalability. The goal of s-step algorithms is to reduce the harmful influence of dot products on the parallel performance by grouping several of these operations for joint execution; thus, plummeting synchronization time when using a large number of processes. This paper extends the non-symmetric s-step Lanczos method introduced by Kim and Chronopoulos (J. Comput. Appl. Math., 42(3), 357–374, 1992) by a novel normalization scheme. Compared to the unnormalized algorithm, the normalized variant improves numerical stability and reduces the possibility of breakdowns.

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Author information

Authors and Affiliations

  1. University of Freiburg, 79098, Freiburg, Germany

    Stefan Feuerriegel

  2. Friedrich Schiller University Jena, 07743, Jena, Germany

    H. Martin Bücker

Authors
  1. Stefan Feuerriegel
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  2. H. Martin Bücker
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Editor information

Editors and Affiliations

  1. Dipartimento di Ingegneria Industriale e dell’Informazione, Seconda Universita’ di Napoli, 81031, Aversa, Italy

    Rocco Aversa

  2. Institute of Computer Science, Cracow University of Technology, Warszawska 24, 31-155, Cracow, Poland

    Joanna Kołodziej

  3. School of Information Technology, Deakin University, Waurn Ponds, VA, Australia

    Jun Zhang

  4. Ingegnerial Elettrica e Tecnologie dell’ Infomazione, Università degli Studi sdi Napoli Federico II, 80125, Naples, Italy

    Flora Amato

  5. DIMES, Università della Calabria, via P. Bucci 41c, 87036, Rende, CS, Italy

    Giancarlo Fortino

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Feuerriegel, S., Bücker, H.M. (2013). A Normalization Scheme for the Non-symmetric s-Step Lanczos Algorithm. In: Aversa, R., Kołodziej, J., Zhang, J., Amato, F., Fortino, G. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2013. Lecture Notes in Computer Science, vol 8286. Springer, Cham. https://doi.org/10.1007/978-3-319-03889-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-03889-6_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03888-9

  • Online ISBN: 978-3-319-03889-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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