Recursive calculation of dominant singular subspaces.

Chahlaoui, Younes and Gallivan, Kyle A and Van Dooren, Paul (2003) Recursive calculation of dominant singular subspaces. SIAM Journal on Matrix Analysis and Applications (SIMAX), 25 (2). pp. 445-463. ISSN 0895-4798

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Abstract

In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on each column of the matrix, we use a variant of the classical Gram–Schmidt algorithm to estimate this subspace. The method is shown to be particularly suited for matrices with many more rows than columns. Bounds for the accuracy of the computed subspace are provided. Moreover, the analysis of error propagation in this algorithm provides new insights in the loss of orthogonality typically observed in the classical Gram–Schmidt method.

Item Type: Article
Uncontrolled Keywords: AMS subject classifications. 15A18, 15A42, 65Y20
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Younes Chahlaoui
Date Deposited: 10 Feb 2008
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1036

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