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Sbornik: Mathematics, 2003, Volume 194, Issue 6, Pages 941–954
DOI: https://doi.org/10.1070/SM2003v194n06ABEH000747 (Mi sm747) 		 
This article is cited in 73 scientific papers (total in 73 papers)

Tensor approximations of matrices generated by asymptotically smooth functions

E. E. Tyrtyshnikov

Institute of Numerical Mathematics, Russian Academy of Sciences
English version PDF (197 kB) Citations (73)
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DOI: https://doi.org/10.1070/SM2003v194n06ABEH000747
Abstract: For a broad class of matrices (discrete analogues of typical integral operators) their approximability by a sum of direct products of matrices of smaller size is demonstrated. Estimates of the number of terms (the tensor rank) and the corresponding error are obtained. It is shown that, as a method of data compression, tensor approximations provide superlinear compression.
Received: 31.10.2002
Russian version:
Matematicheskii Sbornik, 2003, Volume 194, Number 6, Pages 147–160
DOI: https://doi.org/10.4213/sm747
Bibliographic databases:
UDC: 512.64+517.5
MSC: Primary 15A45, 15A72; Secondary 65F05, 65F30
Language: English
Original paper language: Russian
Citation: E. E. Tyrtyshnikov, “Tensor approximations of matrices generated by asymptotically smooth functions”, Mat. Sb., 194:6 (2003), 147–160; Sb. Math., 194:6 (2003), 941–954
Citation in format AMSBIB
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    • This publication is cited in the following 73 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:1566
    Russian version PDF:587
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    References:101
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