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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.
