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Matrix Computations Using Quasirandom Sequences

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

The convergence of Monte Carlo method for numerical integration can often be improved by replacing pseudorandom numbers (PRNs) with more uniformly distributed numbers known as quasirandom numbers(QRNs). Standard Monte Carlo methods use pseudorandom sequences and provide a convergence rate of O(N-1/2) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)k)N-1).

In this paper we study the possibility of using QRNs for computing matrix-vector products, solving systems of linear algebraic equations and calculating the extreme eigenvalues of matrices. Several algorithms using the same Markov chains with different random variables are described. We have shown, theoretically and through numerical tests, that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the corresponding Monte Carlo methods. Numerical tests are performed on sparse matrices using PRNs and Soboĺ, Halton, and Faure QRNs.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, Florida State University, 203 Love Building, FL 32306-4530, Tallahassee, USA

    Michael Mascagni & Aneta Karaivanova

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

    Aneta Karaivanova

Authors
  1. Michael Mascagni
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  2. Aneta Karaivanova
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Mascagni, M., Karaivanova, A. (2001). Matrix Computations Using Quasirandom Sequences. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_65

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  • DOI: https://doi.org/10.1007/3-540-45262-1_65

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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