Analysis of the Euclidean direction set adaptive algorithm

A mathematical analysis is performed on a previously reported gradient-based adaptive algorithm named the Euclidean direction set (EDS) method. It has been shown that the EDS algorithm has a computational complexity of O(N) for each system update, and a rate of convergence (based on computer simulations) comparable to the RLS algorithm. The stability of the EDS method is studied and it is shown that the algorithm converges to the true solution. It is also proved that the convergence rate of the EDS method is superior to that of the steepest descent method.