The Aitken's acceleration is one of the most commonly used method to speed up the fixed-point iteration computation, including the EM algorithm. However, it requires to compute or approximate the Jacobian of the EM mapping matrix, which can be intractable for complex models. We will present our current research topic, the triple-jump acceleration, to accelerate the EM and some of its extrapolation-based variants by approximating their Jacobians. One advantage of the triple jump framework is that we can directly use the EM and its extrapolation-based variants as black boxes and achieve acceleration easily. We can update parameter vectors globally with the same approximated Jacobian, or locally based on each decomposable component with different Jacobians. Experimental results show that the triple jump methods consistently accelerate EM, parameterized EM (pEM) and adaptive EM (aEM) for a variety of probabilistic models.