论文信息 - On the qd-type discrete hungry Lotka-Volterra system and its application to the matrix eigenvalue algorithm

On the qd-type discrete hungry Lotka-Volterra system and its application to the matrix eigenvalue algorithm

The discrete hungry Lotka-Volterra (dhLV) system is already shown to be applied to matrix eigenvalue algorithm. In this paper, we discuss a form of the dhLV system named as the qd-type dhLV system and associate it with a matrix eigenvalue computation. Along a way similar to the dqd algorithm, we also design a new algorithm without cancellation in terms of the qd-type dhLV system.

Yoshimasa Nakamura | Masashi Iwasaki | Emiko Ishiwata | Akiko Fukuda

[1] Moody T. Chu,et al. Linear algebra algorithms as dynamical systems , 2008, Acta Numerica.

[2] S. Tsujimoto. An extension and discretization of Volterra equation I , 1993 .

[3] Yoshimasa Nakamura,et al. The Discrete Relativistic Toda Molecule Equation and a Padé Approximation Algorithm , 2001, Numerical Algorithms.

[4] W. Symes. The QR algorithm and scattering for the finite nonperiodic Toda Lattice , 1982 .

[5] Yoshimasa Nakamura,et al. Calculating Laplace Transforms in Terms of the Toda Molecule , 1998, SIAM J. Sci. Comput..

[6] Yoshimasa Nakamura,et al. The discrete hungry Lotka–Volterra system and a new algorithm for computing matrix eigenvalues , 2008 .

[7] Yoshimasa Nakamura,et al. An application of the discrete Lotka–Volterra system with variable step-size to singular value computation , 2004 .

[8] Martin H. Gutknecht,et al. Lectures On Numerical Mathematics , 1990 .