Convergence rate analysis of fast predictor-based least squares algorithm

The numerical stability and convergence rate properties of least mean square (LMS) and recursive least squares (RLS) algorithms have attracted much interest in the literature, however, very few investigations have been reported concerning the fast Newton transversal filter (FNTF) algorithm. The FNTF algorithm spans the range of adaptive algorithm from LMS to RLS and is, therefore, more flexible in implementation. One of the reasons for the lack of analysis of FNTF seems that its derivation is much more complicated since it is based on the min-max principle under the assumption that the input signal is autoregressive of smaller order than that of the filter. Recently, FNTF has been shown to be almost equivalent to the fast predictor-based LS (FPLS) algorithm which is a complexity-reduced version of the PLS algorithm. In this paper, we evaluate the convergence rate of FPLS by considering the eigenvalues of the transition matrix of the state vector and show that the convergence gets slower as the order of the predictor decreases.