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Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions

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Abstract

Gradient systems on the manifolds of Gaussian and multinomial distributions are shown to be completely integrable Hamiltonian systems. The corresponding flows converge exponentially to equilibrium. A Lax representation of the gradient systems is found.

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Author information

Author notes

  1. Yoshimasa Nakamura

    Present address: Applied Mathematics Laboratory Department of Electronics, Doshisha University, Kamigyo-ku, 602, Kyoto, Japan

Authors and Affiliations

  1. Department of Mathematics, Gifu University, Yanagido, 501-11, Gifu, Japan

    Yoshimasa Nakamura

Authors
  1. Yoshimasa Nakamura
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Additional information

This research was partially supported by Grant-in-Aid for Scientific Research nos. 03804005 and 04804005 from the Japan Ministry of Education, Science, and Culture.

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Nakamura, Y. Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions. Japan J. Indust. Appl. Math. 10, 179 (1993). https://doi.org/10.1007/BF03167571

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  • DOI: https://doi.org/10.1007/BF03167571

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