Tyrtyshnikov, E. E. 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. Cited in 40 Documents MSC: 65F30 Other matrix algorithms (MSC2010) Keywords:approximation by matrices of smaller size; numerical examples; data compression; tensor approximations; superlinear compression PDFBibTeX XMLCite \textit{E. E. Tyrtyshnikov}, Sb. Math. 194, No. 6, 941--954 (2003; Zbl 1067.65044); translation from Mat. Sb. 194, No. 6, 147--160 (2003) Full Text: DOI