Updating a Rank-Revealing ULV Decomposition
G. W. Stewart · SIAM Journal on Matrix Analysis and Applications · 1993
A ULV decomposition of a matrix A of order n is a decomposition of the form $A = ULV^H $, where U and V are orthogonal matrices and L is a lower triangular matrix. When A is approximately of rank k, the decomposition is rank revealing if the last $n - k$ rows of L are small. This paper presents algorithms for updating a rank-revealing ULV decomposition. The algorithms run in $O( n^2 )$ time, and can be implemented on a linear array of processors to run in $O( n )$ time.