Stability Analysis of Oja-RLS Learning Rule

  • Authors:
  • Radosław Sikora;Władysław Skarbek

  • Affiliations:
  • (Correspd.) Institute of Mathematics, Polish Academy of Sciences;(Correspd.) Faculty of Electronics and Information Technology, Warsaw University of Technology Address: Nowowiejska 15/19, 00-665 Warszawa, POLAND. Email: Skarbek@ire.pw.edu.pl

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 1998

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Abstract

It is shown that the discrete time dynamical system defined by the Oja-RLS algorithm is stable in the closed ring K(0,9/8) - $$\overline{K}$$(0,8/9) if only the initial gain β 0 is bounded by (2B) −1, where B = b 2 and b is the bound for the learning sequence. It is rigorously proved that automatically computed gains β n in Oja-RLS scheme converge to zero with the rate 1/n, almost surely.