ИСТИНА

The main problem with data arrays in many dimensions is that we cannot use them to represent the data in numerical algorithms. Structure and generators become the key issue, and make the construction of algorithms to be kin to many works on structured matrices. The choice of generators is crucial for solving optimization and approximation problems. We consider how matrix approximation results [3] transform into efficient optimization techniques for multi-index arrays with the tensor-train generators [1,2] and virtual dimensions [4]. A new approach based on the TT-CROSS algorithm [2] will be presented for the global optimization task arising in the docking problem. [1] I.Oseledets, E.Tyrtyshnikov, Recursive decomposition of multidimensional tensors, Doklady Mathematics, vol. 80, no. 1 (2009), pp. 460-462. [2] I.Oseledets, E. Tyrtyshnikov, TT-cross approximation for multidimensional arrays, Linear Algebra Appl., 432 (2010), pp. 70-88. [3] S.Goreinov, E.Tyrtyshnikov, Quasioptimality of Skeleton Approximation of a Matrix in the Chebyshev Norm, Doklady Mathematics, vol. 83, no. 3 (2011), pp. 1-2. [4] E.Tyrtyshnikov, Tensor approximations of matrices generated by asymptotically smooth functions, Sbornik Mathematics, vol. 194, no. 5-6 (2003), pp. 941-954. ~ ~