Accelerated euclidean direction search algorithm and related relaxation schemes for solving adaptive filtering problem

The Euclidean direction search (EDS) method is a fairly recent algorithm for solving adaptive filtering problem. The method is a direction set based algorithm, where line searches are perform along Euclidean directions in a cyclic manner in order to search for the minimum of the cost function of the problem. In this paper, the EDS algorithm is described in terms of its relationship with relaxation schemes for solving linear system of equations such as the Gauss-Seidel and Jacobi iterative methods. An acceleration parameter, which is commonly used for such methods, are introduced here and its optimum value derived for uncorrelated input signals with mean 0. Verification of optimum acceleration parameter is demonstrated in the framework of an adaptive system modeling problem.