Open Access
October 2006 Accurate Computation of Singular Values in Terms of Shifted Integrable Schemes
Masashi Iwasaki, Yoshimasa Nakamura
Japan J. Indust. Appl. Math. 23(3): 239-259 (October 2006).


A new scheme with a shift of origin for computing singular values $\sigma_{k}$ is presented. A shift $\theta$ is introduced into the recurrence relation defined by the discrete integrable Lotka--Volterra system with variable step-size. A suitable shift strategy is given so that the singular value computation becomes numerically stable. It is proved that variables in the new scheme converge to $\sigma_{k}^{2}-\sum\theta^{2}$. A comparison of the zero-shift and the nonzero-shift routines is drawn. With respect to both the computational time and the numerical accuracy, it is shown that the nonzero-shift routine is more accurate and faster than a credible LAPACK routine for singular values at least in four different types of test matrices.


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Masashi Iwasaki. Yoshimasa Nakamura. "Accurate Computation of Singular Values in Terms of Shifted Integrable Schemes." Japan J. Indust. Appl. Math. 23 (3) 239 - 259, October 2006.


Published: October 2006
First available in Project Euclid: 11 December 2007

zbMATH: 1117.65055
MathSciNet: MR2281507

Keywords: discrete Lotka--Volterra system , shift of origin , Singular value

Rights: Copyright © 2006 The Japan Society for Industrial and Applied Mathematics

Vol.23 • No. 3 • October 2006
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