Optimal order EDS and FEDS algorithms

This paper is based on a recently published class of adaptive filtering algorithms, namely, the Euclidean direction search (EDS) algorithms. The computationally efficient version is called the fast Euclidean direction search (FEDS) algorithm with a computational complexity of O(N). In this paper, we present two new algorithms called the optimal Euclidean direction search (OEDS) and the optimal fast Euclidean direction search (OFEDS). The optimal algorithms search all the Euclidean directions in each iteration to find the direction giving the greatest decrease of the cost function. In order to reduce the computational complexity, some sub-optimal methods based on the same principle are also discussed. Computer simulation results illustrate that the optimal and suboptimal algorithms converge faster than the original EDS and FEDS algorithms, but achieve the same steady state mean square error.