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Implementation of Monte Carlo algorithms for eigenvalue problem using MPI

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Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1497))

Abstract

The problem of evaluating the dominant eigenvalue of real matrices using Monte Carlo numerical methods is considered.

Three almost optimal Monte Carlo algorithms are presented:

  • Direct Monte Carlo algorithm (DMC) for calculating the largest eigenvalue of a matrix A. The algorithm uses iterations with the given matrix.

  • Resolvent Monte Carlo algorithm (RMC) for calculating the smallest or the largest eigenvalue. The algorithm uses Monte Carlo iterations with the resolvent matrix and includes parameter controlling the rate of convergence;

  • Inverse Monte Carlo algorithm (IMC) for calculating the smallest eigenvalue. The algorithm uses iterations with inverse matrix.

Numerical tests are performed for a number of large sparse test matrices using MPI on a cluster of workstations.

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Author information

Authors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev St.,bl. 25 A, 1113, Sofia, Bulgaria

    I. Dimov & A. Karaivanova

  2. Department of Computer Science, University of Liverpool, Chadwick Building Peach Street, L69 7ZF, Liverpool, UK

    V. Alexandrov

Authors
  1. I. Dimov
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  2. V. Alexandrov
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  3. A. Karaivanova
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Editor information

Vassil Alexandrov Jack Dongarra

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© 1998 Springer-Verlag Berlin Heidelberg

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Dimov, I., Alexandrov, V., Karaivanova, A. (1998). Implementation of Monte Carlo algorithms for eigenvalue problem using MPI. In: Alexandrov, V., Dongarra, J. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 1998. Lecture Notes in Computer Science, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056594

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  • DOI: https://doi.org/10.1007/BFb0056594

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65041-6

  • Online ISBN: 978-3-540-49705-9

  • eBook Packages: Springer Book Archive

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