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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
79/2009

Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions

Boris N. Khoromskij and Ivan V. Oseledets

Abstract

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.

Received:
Dec 16, 2009
Published:
Dec 16, 2009
MSC Codes:
65F50, 65F30, 46B28, 47A80
Keywords:
high dimensions, tensor approximation, boundary value problems, quantics and tensor train formats, elliptic inverse, spectral problems

Related publications

inJournal
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