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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 11, Issue 3 (Jan 2011)


DMRG Approach to Fast Linear Algebra in the TT-Format

Ivan Oseledets
  • Institute of Numerical Mathematics, Russian Academy of Sciences, 8 Gubkin Street, Moscow, Russia.
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In this paper, the concept of the DMRG minimization scheme is extended to several important operations in the TT-format, like the matrix-by-vector product and the conversion from the canonical format to the TT-format. Fast algorithms are implemented and a stabilization scheme based on randomization is proposed. The comparison with the direct method is performed on a sequence of matrices and vectors coming as approximate solutions of linear systems in the TT-format. A generated example is provided to show that randomization is really needed in some cases. The matrices and vectors used are available from the author or at http://spring.inm.ras.ru/osel

Keywords: Tensors; high-dimensional problem; SVD; TT-format

About the article

Received: 2011-06-14

Revised: 2011-08-16

Accepted: 2011-08-21

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2011-0021.

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© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 4.0

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