Reliable methods in adaptive filtering require introduction of redundancy into the design of adaptive filter structures. Unfortunately, this form of redundancy can severely impair the convergence rate of the adaptive filtering algorithm. The covariance matrix of the input to the adaptive filter becomes ill-conditioned due to the introduction of redundancy. Recently, affine projection, and accelerated data reusing algorithms have been proposed as a viable methods to accelerate performance in situations where the auto-correlation matrix becomes ill-conditioned. In this paper, some of these methods are explored to accelerate the performance of fault tolerant algorithms. The use of these acceleration algorithms can be seen to significantly improve the performance over that achieved by conventional LMS and LMS-transform domain fault tolerant algorithms.