Minimum singular value estimation of bipolar matrices
ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
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The usual way to compute a low-rank approximant of a matrix $H$ is to take its singular value decomposition (SVD) and truncate it by setting the small singular values equal to 0. 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 $d$ approximants $\Ha$ such that $H - \Ha$ 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 a description 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.