Abstract
A new scheme with a shift of origin for computing singular values σk is presented. A shift θ 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 σ 2 k - Σ θ2. 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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Iwasaki, M., Nakamura, Y. Accurate computation of singular values in terms of shifted integrable schemes. Japan J. Indust. Appl. Math. 23, 239 (2006). https://doi.org/10.1007/BF03167593
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DOI: https://doi.org/10.1007/BF03167593