Superquadratic convergence of DLASQ for computing matrix singular values

DLASQ is a routine in LAPACK for computing the singular values of a real upper bidiagonal matrix with high accuracy. The basic algorithm, the so-called dqds algorithm, was first presented by Fernando-Parlett, and implemented as the DLASQ routine by Parlett-Marques. DLASQ is now recognized as one of the most efficient routines for computing singular values. In this paper, we prove the asymptotic superquadratic convergence of DLASQ in exact arithmetic.