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International Conference on Large-Scale Scientific Computing

LSSC 2003: Large-Scale Scientific Computing pp 128–135Cite as

A New Quasi-Monte Carlo Algorithm for Numerical Integration of Smooth Functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2907))

Abstract

Bachvalov proved that the optimal order of convergence of a Monte Carlo method for numerical integration of functions with bounded kth order derivatives is \(\mathop{O}\left(N^{-\frac{k}{s}-\frac{1}{2}}\right)\), where s is the dimension. We construct a new Monte Carlo algorithm with such rate of convergence, which adapts to the variations of the sub-integral function and gains substantially in accuracy, when a low-discrepancy sequence is used instead of pseudo-random numbers.

Theoretical estimates of the worst-case error of the method are obtained.

Experimental results, showing the excellent parallelization properties of the algorithm and its applicability to problems of moderately high dimension, are also presented.

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Author information

Authors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bontchev, Bl. 25A, 1113, Sofia, Bulgaria

    Emanouil I. Atanassov, Ivan T. Dimov & Mariya K. Durchova

Authors
  1. Emanouil I. Atanassov
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  2. Ivan T. Dimov
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  3. Mariya K. Durchova
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

  4. Center of Applied Mathematics and Informatics, University of Rousse, 7017, Rousse, Bulgaria

    Plamen Yalamov

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© 2004 Springer-Verlag Berlin Heidelberg

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Atanassov, E.I., Dimov, I.T., Durchova, M.K. (2004). A New Quasi-Monte Carlo Algorithm for Numerical Integration of Smooth Functions. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2003. Lecture Notes in Computer Science, vol 2907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24588-9_13

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  • DOI: https://doi.org/10.1007/978-3-540-24588-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21090-0

  • Online ISBN: 978-3-540-24588-9

  • eBook Packages: Springer Book Archive

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