A Convergence Analysis on URV Refinement
arXiv:1803.09352h-index: 4
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Theoretical improvement for numerical linear algebra practitioners using URV decompositions.
The paper provides a new proof of convergence for the refinement iteration used in Stewart's URV decomposition algorithm, under weaker assumptions than previous work.
Recently, Stewart gave an algorithm for computing a rank revealing URV decomposition of a rectangular matrix. His method makes use of a refinement iteration to achieve an improved estimate of the smallest singular value and its corresponding singular vectors of the matrix. Here, a new proof is given for the convergence of the refinement iteration. This analysis is carried out under slightly weaker assumptions than those of Mathias and Stewart.