Multiplicative nonholonomic/Newton-like algorithm

Toshinao Akuzawa, Noboru Murata

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We construct new algorithms, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has numerous merits for the rigorous treatment of the dynamics. As one consequence, the second order convergence is shown. For the cost function, functions invariant under the componentwise scaling are chosen. By identifying points which can be transformed to each other by the scaling, we assume that the dynamics is in a coset space. In our method, a point can move toward any direction in this coset. Thus, no prewhitening is required.

Original languageEnglish
Pages (from-to)785-793
Number of pages9
JournalChaos, solitons and fractals
Issue number4
Publication statusPublished - 2001 Jan 3
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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