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A Parallel Factorization for Generating Orthogonal Matrices

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Book cover Parallel Processing and Applied Mathematics (PPAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12043))

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Abstract

A new factorization of orthogonal matrices is proposed that is based on Givens-Jacobi rotations but not on the QR decomposition. Rotations are arranged more uniformly than in the known factorizations that use them, so that more rotations can be computed in parallel, and fewer layers of concurrent rotations are necessary to model a matrix. Therefore, throughput can be increased, and latency can be reduced, compared to the known solutions, even though the obtainable gains highly depend on application specificity, software-hardware architecture and matrix size. The proposed approach allows for developing more efficient algorithms and hardware for generating random matrices, for optimizing matrices, and for processing data with linear transformations. We have verified this by implementing and evaluating a multithreaded Java application for generating random orthogonal matrices.

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Acknowledgments

This work was financially supported from the Polish Ministry of Science and Higher Education under subsidy for maintaining the research potential of the Faculty of Mathematics and Informatics, University of Bialystok.

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Authors and Affiliations

  1. University of Bialystok, K. Ciolkowskiego 1M, 15-245, Bialystok, Poland

    Marek Parfieniuk

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  1. Marek Parfieniuk
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Correspondence to Marek Parfieniuk .

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Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Southern California, Marina del Rey, CA, USA

    Ewa Deelman

  3. University of Tennessee, Knoxville, TN, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Parfieniuk, M. (2020). A Parallel Factorization for Generating Orthogonal Matrices. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12043. Springer, Cham. https://doi.org/10.1007/978-3-030-43229-4_48

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  • DOI: https://doi.org/10.1007/978-3-030-43229-4_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43228-7

  • Online ISBN: 978-3-030-43229-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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