Modifiable low-rank approximation to a matrix
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A truncated ULV decomposition (TULVD) of an m x n matrix X of rank k is a decomposition of the form X=ULVT + E, where U and V are left orthogonal matrices, L is a k x k non-singular lower triangular matrix and E is an error matrix. Only U,V, L and parallel to E parallel to(F) are stored, but E is not stored. We propose algorithms for updating and downdating the TULVD. To construct these modification algorithms, we also use a refinement algorithm based upon that in (SIAM J. Matrix Anal. Appl. 2005; 27(1):198-211) that reduces parallel to E parallel to(F), detects rank degeneracy, corrects it, and sharpens the approximation. Copyright (C) 2009 John Wiley & Sons, Ltd.