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Tensor approximations of matrices generated by asymptotically smooth functions. (English. Russian original) Zbl 1067.65044

Sb. Math. 194, No. 6, 941-954 (2003); translation from Mat. Sb. 194, No. 6, 147-160 (2003).
Summary: 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.

MSC:

65F30 Other matrix algorithms (MSC2010)
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