Fast and accurate numerical algorithms for Eigen-Value Decomposition (EVD) are of great importance in solving many engineering problems. In this paper, we aim to develop algorithms for finding the leading eigen pairs with improved convergence speed compared to existing methods. We introduce several accelerated methods based on the power iterations where the main modification is to introduce a memory term in the iteration, similar to Nesterov's acceleration. Results on convergence and the speed of convergence are presented on a proposed method termed Memory-based Accelerated Power with Scaling (MAPS). Nesterov's acceleration for the power iteration is also presented. We discuss possible application of the proposed algorithm to (distributed) clustering problems based on spectral clustering. Simulation results show that the proposed algorithms enjoy faster convergence rates than the power method for matrix eigen-decomposition problems.