Preprint 79/2009

Quantics-TT Approximation of Elliptic Solution Operators in Higher Dimensions

Boris N. Khoromskij and Ivan V. Oseledets

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Submission date: 16. Dec. 2009 (revised version: January 2010)
Pages: 18
published in: Russian journal of numerical analysis and mathematical modelling, 26 (2011) 3, p. 303-322 
DOI number (of the published article): 10.1515/RJNAMM.2011.017
with the following different title: QTT approximation of elliptic solution operators in higher dimensions
MSC-Numbers: 65F50, 65F30, 46B28, 47A80
Keywords and phrases: high dimensions, tensor approximation, boundary value problems, quantics and tensor train formats, elliptic inverse, spectral problems
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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 formula4-accurate solutions in the Frobenius norm can be computed with the complexity formula6, where formula8 is some fixed constant. This seems to be the nearly optimal computational cost to be expected in the d-dimensional numerical simulations.

18.10.2019, 02:14