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International Conference on Parallel Computing Technologies

PaCT 2009: Parallel Computing Technologies pp 147–152Cite as

Parallel Algorithms of Numeric Integration Using Lattice Cubature Formulas

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5698))

Abstract

The results of theory and applications of optimal lattice cubature formulas are described. The approximate integration program based on lattice formulas is considered. It has sufficiently high precision for complicated domains with smooth boundaries and dimensions up to 10 and high efficiency of paralleling.

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References

  1. Sobolev, S.L.: Introduction to the Theory of Cubature Formulas. Nauka, Moscow (1974) (in Russian)

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  2. Ramazanov, M.D.: To the L p -theory of Sobolev Formulas. Siberian Advances in Mathematics 9(1), 99–125 (1999)

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  3. Ramazanov, M.D.: Optimization of the Lattice Cubature Formula Error Functional Norm in Scale of Wiener Spaces. Reports of Russian Academy of Sciences 36(6), 743–745 (1997) (in Russian)

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  4. Ramazanov, M.D.: The Cubature Formulas of S.L. Sobolev: The Evolution of the Theory and Applications. In: International Conference on Multivariate Approximation, Haus Bommerholz, p. 33. Tech. Univ. Dortmund (2008)

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  5. Rakhmatullin, D.Y.: Integration on Multidimensional Spaces on Multiprocessing Calculating Systems. Vychislitel’nye tehnologii 11(3), 118–125 (2006) (in Russian)

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Author information

Authors and Affiliations

  1. Institute of Mathematic with Computing Centre of RAS, 112, Chernyshevsky str., Ufa, Russia, 450008

    Marat D. Ramazanov & Dzhangir Y. Rakhmatullin

Authors
  1. Marat D. Ramazanov
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  2. Dzhangir Y. Rakhmatullin
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Editor information

Editors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Supercomputer Department, Pr. Lavrentieva, ICM&MG RAS, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Victor Malyshkin

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Ramazanov, M.D., Rakhmatullin, D.Y. (2009). Parallel Algorithms of Numeric Integration Using Lattice Cubature Formulas. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2009. Lecture Notes in Computer Science, vol 5698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03275-2_16

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  • DOI: https://doi.org/10.1007/978-3-642-03275-2_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03274-5

  • Online ISBN: 978-3-642-03275-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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