Analysis of the Euclidean direction set adaptive algorithm

A mathematical analysis is performed on a recently 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. In this paper, 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. method is a new gradient-based adaptive process and it can be implemented by a Euclidean direction search procedure. A mathematical analysis of stability and convergence rate are presented in Section 3. Concluding remarks are given in Section 4. 2. EUCLIDEAN DIRECTION SET METHOD Consider the following quadratic optimization problem, J(W) = mkN (W=RW 2WTP + d}, (1) where R is an N x N real symmetric positive definite matrix (Hessian); P and variable W are vectors of order N, and d is a scaler. The notation (.)= means the transpose of (.).