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Jacobi algorithm for symmetric eigenvalue problem and integrable gradient system of Lax form

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Abstract

An intimate connection between matrix eigenvalue algorithms and integrable dynamical systems is studied. It is proved that an infinitesimal rotation of each step of the Jacobi algorithm for symmetric eigenvalue problem is an integrable gradient system of Lax form.

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Author notes

  1. Yoshimasa Nakamura

    Present address: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, 560, Toyonaka, Japan

Authors and Affiliations

  1. Department of Electronics, Doshisha University, Tanabe, 610-03, Kyoto, Japan

    Yoshimasa Nakamura

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  1. Yoshimasa Nakamura
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Nakamura, Y. Jacobi algorithm for symmetric eigenvalue problem and integrable gradient system of Lax form. Japan J. Indust. Appl. Math. 14, 159–168 (1997). https://doi.org/10.1007/BF03167262

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  • DOI: https://doi.org/10.1007/BF03167262

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