Schur method for low-rank matrix approximation

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.