On Convergence of the DQDS Algorithm for Singular Value Computation

Authors:
Kensuke Aishima;Takayasu Matsuo;Kazuo Murota;Masaaki Sugihara
Affiliations:
Kensuke_Aishima@mist.i.u-tokyo.ac.jp and matsuo@mist.i.u-tokyo.ac.jp and murota@mist.i.u-tokyo.ac.jp and m_sugihara@mist.i.u-tokyo.ac.jp;-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2008

Citing 0
Cited 3

Superquadratic convergence of DLASQ for computing matrix singular values

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dqds with Aggressive Early Deflation

SIAM Journal on Matrix Analysis and Applications
A shift strategy for superquadratic convergence in the dqds algorithm for singular values

Journal of Computational and Applied Mathematics

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Abstract

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.