ИСТИНА

The future of tensor computations and their advent to various application areas is certainly related with the new findings appeared as recently as just in the beginning of 2009, called tensor-train decomposions and algorithms. The purpose of this talk is to present the vistas of tensor-train algorithms, in particular the interpolation properties of tensor trains and relations with the matrix interpolation problems, pseudo-skeleton approximations, and the maximal-volume concept in low-rank approximations of matrices. For more details see http://pub.inm.ras.ru and the following references: [1] I.Oseledets, E.Tyrtyshnikov, Recursive decomposition of multidimensional tensors, Doklady Mathematics, vol. 80, no. 1 (2009), pp. 460-462. [2] N.Zamarashkin, I.Oseledets, E.Tyrtyshnikov, The tensor structure of the inverse of a banded Toeplitz matrix, Doklady Mathematics, vol. 80, no. 2 (2009), pp. 669-670. [3] I. Oseledets, E. Tyrtyshnikov, Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput., vol 31, no. 5 (2009), pp. 3744-3759. [4] I. Oseledets, E. Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra Appl., 432 (2010), pp. 70-88.