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High-Performance Scientific Computing pp 185–197Cite as

Parallel Block-Jacobi SVD Methods

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Abstract

The serial Jacobi algorithm (either one-sided or two-sided) for the computation of a singular value decomposition (SVD) of a general matrix has excellent numerical properties and parallelization potential, but it is considered to be the slowest method for computing the SVD. Even its parallelization with some parallel cyclic (static) ordering of subproblems does not lead to much improvement when comparing with parallel methods based on the matrix bi-diagonalization principle. However, in the last 10 years some progress has been achieved in increasing the efficiency of the parallel block-Jacobi SVD method by using two new ideas: (i) the new parallel dynamic ordering of subproblems, and, (ii) the matrix pre-processing by QR iterations. For the parallel two-sided block-Jacobi algorithm, these ideas were already thoroughly tested on various parallel platforms, and our implementation can be faster than the ScaLAPACK routine PDGESVD for some distributions of singular values. With respect to the one-sided variant, the new parallel dynamic ordering, when compared to parallel cyclic ordering, can substantially decrease the number of parallel iteration steps needed for the convergence. However, its more scalable implementation is desirable because currently it occupies a relatively high portion of the total parallel execution time.

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Acknowledgements

The authors were supported by the VEGA grant no. 2/0003/11 from the Scientific Grant Agency of the Ministry of Education and Slovak Academy of Sciences, Slovakia.

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Authors and Affiliations

  1. Mathematical Institute, Department of Informatics, Slovak Academy of Sciences, Bratislava, Slovak Republic

    Martin Bečka, Gabriel Okša & Marián Vajteršic

  2. Department of Computer Sciences, University of Salzburg, Salzburg, Austria

    Marián Vajteršic

Authors
  1. Martin Bečka
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  2. Gabriel Okša
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  3. Marián Vajteršic
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Corresponding author

Correspondence to Martin Bečka .

Editor information

Editors and Affiliations

  1. Dept. Electrical Eng. & Computer Science, University of Tennessee, Volunteer Boulevard 1122, Knoxville, 37996-3450, Tennessee, USA

    Michael W. Berry

  2. Department of Mathematics, Florida State University, Academic Way 1017, Tallahassee, 32306, Florida, USA

    Kyle A. Gallivan

  3. Dept. Computer Engineering & Informatics, University of Patras, Patras, 26500, Greece

    Efstratios Gallopoulos

  4. Department of Computer Science, Purdue University, 305 North University Street, West Lafayette, 47907-2107, Indiana, USA

    Ananth Grama

  5. IRISA, INRIA Rennes - Bretagne Atlantique, Campus de Beaulieu, Rennes, 35042, France

    Bernard Philippe

  6. Dept. of Computer Science & Engineering, University of Minnesota, Union Street SE 200, Minneapolis, 55455, Minnesota, USA

    Yousef Saad

  7. Department of Computer Science, Purdue University, N. University Street 305, West Lafayette, 47907-2107, Indiana, USA

    Faisal Saied

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© 2012 Springer-Verlag London Limited

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Bečka, M., Okša, G., Vajteršic, M. (2012). Parallel Block-Jacobi SVD Methods. In: Berry, M., et al. High-Performance Scientific Computing. Springer, London. https://doi.org/10.1007/978-1-4471-2437-5_9

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  • DOI: https://doi.org/10.1007/978-1-4471-2437-5_9

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2436-8

  • Online ISBN: 978-1-4471-2437-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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