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
Bibtex
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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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 -accurate solutions in the Frobenius norm can be computed with the complexity , where is some fixed constant. This seems to be the nearly optimal computational cost to be expected in the d-dimensional numerical simulations.