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In this paper, we derive a new similarity transformation from the discrete Lotka–Volterra system by taking an infinite limit of the discretization parameter. The proposed similarity transformation is shown to be applicable for computing singular values of a bidiagonal matrix. The forward stability of it is also verified in floating point arithmetic.
Some of the authors show in Iwasaki and Nakamura (Inverse Probl 20:553–563, 2004) that the integrable discrete Lotka–Volterra (dLV) system is applicable for computing singular values of bidiagonal matrix. The resulting numerical algorithm is referred to as the dLV algorithm. They also observe in Iwasaki and Nakamura (Electron Trans Numer Anal 38:184–201, 2011) that the singular values are numerically...
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