Downdating the Rank-Revealing URV Decomposition

An accurate algorithm is presented for downdating a row in the rank-revealing URV decomposition that was recently introduced by Stewart. By downdating the full rank part and the noise part in two separate steps, the new algorithm can produce accurate results even for ill-conditioned problems. Such problems occur, for example, when the rank of the matrix is decreased as a consequence of the downdate. Other possible generalizations of existing QR decomposition downdating algorithms for the rank-revealing URV downdating are discussed. Numerical test results are presented that compare the performance of these new URV decomposition downdating algorithms in the sliding window method.