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

  • Yoshimasa Nakamura
Article

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.

Key words

integrable gradient systems integrable Hamiltonian systems Lax representation Gaussian distributions multinomial distributions information geometry 

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Copyright information

© JJIAM Publishing Committee 1993

Authors and Affiliations

  • Yoshimasa Nakamura
    • 1
  1. 1.Department of MathematicsGifu UniversityGifuJapan

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