Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 2, Pages 131–140 (Mi sjvm431)  
This article is cited in 2 scientific papers (total in 2 papers)

Analytical description for application of 1D Kohonen scheme for constructing adaptive meshes

A. V. Voytishekab, D. S. Khmelb

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
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Abstract: In this paper, the analysis of analytical approaches to investigation of an asymptotical disposition for a special iterative discrete-stochastic algorithm for constructing adaptive meshes using the Kohonen self-organizing maps is made. For a simplified one-dimensional case, a “recurrent” approach to obtaining mean most probable dispositions of grid nodes for a small number of iterations has been developed. This approach allows one to conduct interesting analytical investigations and numerical testing for the algorithm considered.
Key words: Kohonen self-organizing maps, adaptive meshes, discretely-stochastic algorithm, simplified 1D case, recurrent formulas for mean most probable dispositions of grid nodes.
Received: 13.09.2010
Revised: 24.10.2010
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 2, Pages 105–113
DOI: https://doi.org/10.1134/S1995423911020029
Bibliographic databases:
Document Type: Article
UDC: 519.676
Language: Russian
Citation: A. V. Voytishek, D. S. Khmel, “Analytical description for application of 1D Kohonen scheme for constructing adaptive meshes”, Sib. Zh. Vychisl. Mat., 14:2 (2011), 131–140; Num. Anal. Appl., 4:2 (2011), 105–113
Citation in format AMSBIB
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\by A.~V.~Voytishek, D.~S.~Khmel
\paper Analytical description for application of 1D Kohonen scheme for constructing adaptive meshes
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 2
\pages 131--140
\mathnet{http://mi.mathnet.ru/sjvm431}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 2
\pages 105--113
\crossref{https://doi.org/10.1134/S1995423911020029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79957822198}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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