Schur method for low-rank matrix approximation

Alle-Jan van der Veen

doi:10.1117/12.190848

28 October 1994 Schur method for low-rank matrix approximation

Alle-Jan van der Veen

Proceedings Volume 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V; (1994) https://doi.org/10.1117/12.190848
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

The usual way to compute a low-rank approximant of a matrix H is to take its truncated SVD. However, the SVD is computationally expensive. This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants. For a given matrix H which has d singular values larger than (epsilon) , we find all rank d approximate H such that H - H has 2-norm less than (epsilon) . The set of approximants includes the truncated SVD approximation. The advantages of the Schur algorithm are that it has a much lower computational complexity (similar to a QR factorization), and directly produces estimates of the column space of the approximants. This column space can be updated and downdated in an on-line scheme, amenable to implementation on a parallel array of processors.

Citation Download Citation

Alle-Jan van der Veen "Schur method for low-rank matrix approximation", Proc. SPIE 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, (28 October 1994); https://doi.org/10.1117/12.190848

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