ECM algorithms that converge at the rate of EM

We show that the ECM algorithm can always be constructed to converge at the same or approximately the same rate as the Ehl algorithm. The construction is based on the well-known conjugate directions algorithm. This result bot h suggests ways of speeding up the convergence of ECM and provides a simple way of identifying cases where the simplicity and stability of ECM over EM is attained at effectively no loss in convergence speed. Three examples ar e given.