An efficient rank detection procedure for modifying the ULV decomposition (Q1279702)

ULVD is a rank-revealing tow-sided orthogonal decomposition that is used to approximate the singular value decomposition (SVD) of a matrix. The authors propose an algorithm which, almost always, maintains rank-revealing structure of the decomposition, after an update or down-date without standard condition estimation. The algorithm makes it possible to monitor the accuracy of the information obtained by ULVD in comparison with the SVD by tracking the norms of two small blocks of lower triangular factors in the decomposition. Numerical examples are given illustrating the use of the proposed algorithm.