Abstract
We consider the problem of the decomposition of an underdetermined source into a product of sources generating the symbols 0, 1, and the indefinite symbol *. We also study the problem of the best approximate decomposition (in a prescribed sense) if no exact decomposition is possible. It is proved that the best approximate decomposition exists and is unique up to some equivalence for every underdetermined source (for a decomposable source, it is its decomposition). A polynomial algorithm is described for constructing the best approximate decomposition. We study the problems connected with simplification and equivalent transformations of decompositions and propose some polynomial algorithms.
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Original Russian Text © L.A. Sholomov, 2012, published in Diskretnyi Analiz i Issledovanie Operatsii, 2012, Vol. 19, No. 6, pp. 72–98.
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Sholomov, L.A. Decomposition of underdetermined data. J. Appl. Ind. Math. 7, 100–116 (2013). https://doi.org/10.1134/S1990478913010109
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DOI: https://doi.org/10.1134/S1990478913010109