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 Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 2, Pages 211–216 (Mi zvmmf10829)

Tensor trains approximation estimates in the Chebyshev norm

A. I. Osinskii

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, 119333 Russia

Abstract: A new elementwise bound on the cross approximation error used for approximating multi-index arrays (tensors) in the format of a tensor train is obtained. The new bound is the first known error bound that differs from the best bound by a factor that depends only on the rank of the approximation $r$ and on the dimensionality of the tensor $d$, and the dependence on the dimensionality at a fixed rank has only the order $d^{\operatorname{const}}$ rather than $\operatorname{const}^d$. Thus, this bound justifies the use of the cross method even for high dimensional tensors.

Key words: multidimensional arrays, nonlinear approximations, maximum volume principle.

 Funding Agency Grant Number Russian Science Foundation 14-11-00806 This work was supported by the Russian Science Foundation, project no. 14-11-00806.

DOI: https://doi.org/10.1134/S0044466919020121

English version:
Computational Mathematics and Mathematical Physics, 2019, 59:2, 201–206

Bibliographic databases:

UDC: 517.977

Citation: A. I. Osinskii, “Tensor trains approximation estimates in the Chebyshev norm”, Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019), 211–216; Comput. Math. Math. Phys., 59:2 (2019), 201–206

Citation in format AMSBIB
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