Abstract
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.
Citation
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.
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