Abstract
The predictor-based least squares algorithm (5) derived from the relation of the backward predictors as the fast RLS (FRLS) algorithm [1] gives the exact solution of the least squares problem as the RLS, the FRLS algorithms do. One of its advantages is the possibility of reducing its complexity to O(MN) where N is the length of the filter if the input signal is autoregressive of order M(≪ N) by truncating the prediction filters in the PLS algorithm. This algorithm is named the fast PLS (FPLS) algorithm [7] and is proven to be equivalent to the fast Newton transversal filter (FNTF) algorithm [4]. Since the FPLS and the FNTF algorithms do not rigorously solve the LS problem, they have a different convergence rate from the LS algorithms such as the RLS, the FRLS and the PLS algorithms. This paper theoretically gives the convergence rate, which is larger (slower) than that of the LS algorithms.
