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On the Preconditioned Quasi-Monte Carlo Algorithm for Matrix Computations

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Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

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Abstract

In this paper we present a quasi-Monte Carlo Sparse Approximate Inverse (SPAI) preconditioner. In contrast to the standard deterministic SPAI preconditioners that use the Frobenius norm, Monte Carlo and quasi-Monte Carlo preconditioners rely on stochastic and hybrid algorithms to compute a rough matrix inverse (MI). The behaviour of the proposed algorithm is studied. Its performance is measured and compared with the standard deterministic SPAI and MSPAI (parallel SPAI) approaches and with the Monte Carlo approach. An analysis of the results is also provided.

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Acknowledgment

The research work reported in the paper is partly supported by the Bulgarian NSF grant Grant DFNI-I02/8, and second author would like to thank CONACYT-Mexico for supporting potsdoctoral position in BSC.

Author information

Authors and Affiliations

  1. ICREA-BSC, C/Jordi Girona 29, 08034, Barcelona, Spain

    V. Alexandrov

  2. UNAM, Mexico and Barcelona Supercomputing Centre, Barcelona, Spain

    O. Esquivel-Flores

  3. IICT-BAS, acad. G. Bonchev Street, Bl. 25A, 1113, Sofia, Bulgaria

    S. Ivanovska & A. Karaivanova

Authors
  1. V. Alexandrov
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  2. O. Esquivel-Flores
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  3. S. Ivanovska
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  4. A. Karaivanova
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Corresponding author

Correspondence to A. Karaivanova .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Alexandrov, V., Esquivel-Flores, O., Ivanovska, S., Karaivanova, A. (2015). On the Preconditioned Quasi-Monte Carlo Algorithm for Matrix Computations. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_17

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  • DOI: https://doi.org/10.1007/978-3-319-26520-9_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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