2008.14: Recursive calculation of dominant singular subspaces.
2008.14: Younes Chahlaoui, Kyle A Gallivan and Paul Van Dooren (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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DOI: 10.1137/S0895479803374657
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 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |
| MIMS number: | 2008.14 |
| Deposited By: | Dr Younes Chahlaoui |
| Deposited On: | 10 February 2008 |
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