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SIAM J. on Scientific Computing / Volume 34 / Issue 1 / Methods and Algorithms for Scientific Computing

SIAM J. Sci. Comput. 34, pp. A1-A27 (27 pages)

Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case

S. A. Goreinov, I. V. Oseledets, and D. V. Savostyanov

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New algorithms are proposed for the Tucker approximation of a 3-tensor accessed only through a tensor-by-vector-by-vector multiplication subroutine. In the matrix case, the Krylov methods are methods of choice to approximate the dominant column and row subspaces of a sparse or structured matrix given through a matrix-by-vector operation. Using the Wedderburn rank reduction formula, we propose a matrix approximation algorithm that computes the Krylov subspaces and can be generalized to 3-tensors. The numerical experiments show that on quantum chemistry data the proposed tensor methods outperform the minimal Krylov recursion of Savas and Eldén.

© 2012 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

15A23, 15A69, 65F50, 65F99

PUBLICATION DATA

ISSN

1064-8275 (print)  
1095-7197 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received April 12, 2010
Accepted September 14, 2011
Published online January 31, 2012
Digital Object Identifier
http://dx.doi.org/10.1137/100792056

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