A block QR algorithm and the singular value decomposition

Abstract

In this note we consider an iterative algorithm for moving a triangular matrix toward diagonality. The algorithm is related to algorithms for refining rank-revealing triangular decompositions, and in a variant form, to the QR algorithm. It is shown to converge if there is a sufficient gap in the singular values of the matrix, and the analysis provides a new approximation theorem for singular values and singular subspaces.