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Efficient Evaluation of Matrix Polynomials

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Parallel Processing and Applied Mathematics (PPAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10777))

Abstract

We revisit the problem of evaluating matrix polynomials and introduce memory and communication efficient algorithms. Our algorithms, based on that of Patterson and Stockmeyer, are more efficient than previous ones, while being as memory-efficient as Van Loan’s variant. We supplement our theoretical analysis of the algorithms, with matching lower bounds and with experimental results showing that our algorithms outperform existing ones.

This research is supported by grants 1878/14, 1901/14, 965/15 and 863/15 from the Israel Science Foundation, grant 3-10891 from the Israeli Ministry of Science and Technology, by the Einstein and Minerva Foundations, by the PetaCloud consortium, by the Intel Collaborative Research Institute for Computational Intelligence, by a grant from the US-Israel Bi-national Science Foundation, and by the HUJI Cyber Security Research Center.

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Author information

Authors and Affiliations

  1. Tel-Aviv University, Tel Aviv, Israel

    Niv Hoffman & Sivan Toledo

  2. The Hebrew University of Jerusalem, Jerusalem, Israel

    Oded Schwartz

Authors
  1. Niv Hoffman
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  2. Oded Schwartz
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  3. Sivan Toledo
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Corresponding author

Correspondence to Sivan Toledo .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Hoffman, N., Schwartz, O., Toledo, S. (2018). Efficient Evaluation of Matrix Polynomials. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10777. Springer, Cham. https://doi.org/10.1007/978-3-319-78024-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-78024-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78023-8

  • Online ISBN: 978-3-319-78024-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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