  The ECME algorithm has proven to be an effective way of accelerating the EM
algorithm for many problems. Recognising the limitation of using prefixed
acceleration subspace in ECME, we propose the new Dynamic ECME (DECME)
algorithm which allows the acceleration subspace to be chosen dynamically. Our
investigation of an inefficient special case of DECME, the classical Successive
Overrelaxation (SOR) method, leads to an efficient, simple, and widely
applicable DECME implementation, called DECME_v1. The fast convergence of
DECME_v1 is established by the theoretical result that, in a small
neighbourhood of the maximum likelihood estimate (MLE), DECME_v1 is equivalent
to a conjugate direction method. Numerical results show that DECME_v1 and its
two variants are very stable and often converge faster than EM by a factor of
one hundred in terms of number of iterations and a factor of thirty in terms of
CPU time when EM is very slow.
