Superquadratic convergence of DLASQ for computing matrix singular values

Authors:
Kensuke Aishima;Takayasu Matsuo;Kazuo Murota;Masaaki Sugihara
Affiliations:
University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, Japan;University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, Japan;University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, Japan;University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 8
Cited 1

The algebraic eigenvalue problem

The algebraic eigenvalue problem
Accurate singular values of bidiagonal matrices

SIAM Journal on Scientific and Statistical Computing
Applied numerical linear algebra

Applied numerical linear algebra
The symmetric eigenvalue problem

The symmetric eigenvalue problem
A new O (N(2)) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem

A new O (N(2)) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem
LAPACK Users' guide (third ed.)

LAPACK Users' guide (third ed.)
Orthogonal Eigenvectors and Relative Gaps

SIAM Journal on Matrix Analysis and Applications
On Convergence of the DQDS Algorithm for Singular Value Computation

SIAM Journal on Matrix Analysis and Applications

dqds with Aggressive Early Deflation

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

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.