On Convergence of the DQDS Algorithm for Singular Value Computation
Kensuke Aishima, Takayasu Matsuo, Kazuo Murota, Masaaki Sugihara · SIAM Journal on Matrix Analysis and Applications · 2008
We prove global convergence, in exact arithmetic, for the differential quotient difference algorithm that is currently implemented in LAPACK for the computation of the singular values of a bidiagonal matrix. Our results cover any shift strategy that preserves positivity. We also show that the asymptotic rate for the Johnson shift is 3/2.