A contribution to the theory and practice of the block Kogbetliantz method for computing the SVD

Abstract

This article studies the convergence and practical implementation of the block version of the Kogbetliantz algorithm for computing the singular value decomposition (SVD) of general real or complex matrices. Global convergence is proved for simple singular values and the singular vectors, including the asymptotically quadratic reduction to diagonal form. The convergence can be guaranteed for certain parallel block pivot strategies as well. This bridges a theoretical gap, provides solid theoretical basis for parallel implementations of the block algorithm, and provides valuable insights. © 2012 Springer Science + Business Media B.V.