Stability Analysis of Oja-RLS Learning Rule

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 β₀ is bounded by (2B)⁻¹, where B = b² 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.