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MiS Preprint

Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions

Boris N. Khoromskij and Ivan V. Oseledets


In the present paper, we present the numerical analysis of the quantics-TT (QTT) methods for numerical solution of the elliptic equations in higher dimensions. The $\varepsilon$-accurate solutions in the Frobenius norm can be computed with the complexity $O(d \log^q \varepsilon^{-1})$, where $q\geq 2$ is some fixed constant. This seems to be the nearly optimal computational cost to be expected in the $d$-dimensional numerical simulations.

MSC Codes:
65F50, 65F30, 46B28, 47A80
high dimensions, tensor approximation, boundary value problems, quantics and tensor train formats, elliptic inverse, spectral problems

Related publications

2011 Repository Open Access
Boris N. Khoromskij and Ivan V. Oseledets

QTT approximation of elliptic solution operators in higher dimensions

In: Russian journal of numerical analysis and mathematical modelling, 26 (2011) 3, pp. 303-322