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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2011, Issue 9, Pages 107–118 (Mi vyuru179)  

This article is cited in 4 scientific papers (total in 4 papers)

Programming

The parallel simplex-method achievements for errorless solving of linear programming problems

A. V. Panyukov, V. V. Gorbik

South Ural State University, Chelyabinsk
Full-text PDF (317 kB) Citations (4)
References:
Abstract: Techniques of obtaining exact solutions of linear programming problems are subjects of this paper. Absolute accuracy are arrived at implementation of simplex-algorithm with exact rational-fractional computation. In this case if $m$ is minimal of problem dimensions, and $l$ is number of bits for a source data item then space complexity are no more $4lm^4+o(m^3)$, one iteration time complexity are no more $O(lm^4)$, and paralleling efficiency (i.e. ratio of acceleration to number of processors) asymptotical estimate are 100%.
Keywords: linear programming, simplex method, distributed computing, parallel computing, rational computations, optimization, arbitrary precision, interval arithmetic.
Received: 20.03.2011
Document Type: Article
UDC: 519.852
Language: Russian
Citation: A. V. Panyukov, V. V. Gorbik, “The parallel simplex-method achievements for errorless solving of linear programming problems”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2011, no. 9, 107–118
Citation in format AMSBIB
\Bibitem{PanGor11}
\by A.~V.~Panyukov, V.~V.~Gorbik
\paper The parallel simplex-method achievements for errorless solving of linear programming problems
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2011
\issue 9
\pages 107--118
\mathnet{http://mi.mathnet.ru/vyuru179}
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  • https://www.mathnet.ru/eng/vyuru/y2011/i9/p107
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:293
    Full-text PDF :181
    References:30
     
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