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 Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 1, Pages 200–208 (Mi zvmmf62)

Algebra over estimation algorithms: Normalization with respect to the interval

A. G. D'yakonov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: Algebra over estimation algorithms with addition, multiplication by a constant, and normalization operations is investigated. Normalization is interpreted as a linear (with respect to each row) transformation of the matrix of estimates that takes the maximum entry of the row to unity and the minimum entry to zero. The algebraic closure is described, a formula for its dimension is obtained, and correctness criteria are formulated.

Key words: pattern recognition, estimation algorithm, matrices of estimates, correct algorithm, normalization, algebra over algorithms.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:1, 194–202

Bibliographic databases:

UDC: 519.71

Citation: A. G. D'yakonov, “Algebra over estimation algorithms: Normalization with respect to the interval”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 200–208; Comput. Math. Math. Phys., 49:1 (2009), 194–202

Citation in format AMSBIB
\Bibitem{Dya09} \by A.~G.~D'yakonov \paper Algebra over estimation algorithms: Normalization with respect to the interval \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2009 \vol 49 \issue 1 \pages 200--208 \mathnet{http://mi.mathnet.ru/zvmmf62} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2559756} \transl \jour Comput. Math. Math. Phys. \yr 2009 \vol 49 \issue 1 \pages 194--202 \crossref{https://doi.org/10.1134/S096554250901014X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000263128900014} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-59849107927} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. V. Ablameyko, A. S. Biryukov, A. A. Dokukin, A. G. D'yakonov, Yu. I. Zhuravlev, V. V. Krasnoproshin, V. A. Obraztsov, M. Yu. Romanov, V. V. Ryazanov, “Practical algorithms for algebraic and logical correction in precedent-based recognition problems”, Comput. Math. Math. Phys., 54:12 (2014), 1915–1928
2. M. V. Grishko, A. E. Dyusembaev, “Construction of a correct algorithm and spatial neural network for recognition problems with binary data”, Comput. Math. Math. Phys., 58:10 (2018), 1673–1686
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