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Tensor approximations of matrices generated by asymptotically smooth functions

E. E. Tyrtyshnikov

Institute of Numerical Mathematics, Russian Academy of Sciences

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.

UDC: 512.64+517.5

MSC: Primary 15A45, 15A72; Secondary 65F05, 65F30

Received: 31.10.2002

DOI: 10.4213/sm747

 English version: Sbornik: Mathematics, 2003, 194:6, 941–954

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