For a class of the important problems that seek to maximize the sum rate of the multi-user multiple input multiple output multiple access channel (MIMO MAC) and compute the corresponding optimal input distribution, we developed a more efficient algorithm for solving this class of the problems compared with currently known algorithms. The performance result of this new algorithm indicates that the proposed algorithm overcomes some of the weaknesses of other algorithms. One of the key weaknesses that it overcomes is that the well-known iterative water-filling algorithms cannot utilize the machinery of parallel computation, owning to their inherent structure defects. Not only does the proposed algorithm sufficiently utilizes the machinery of parallel computation, it also shows faster convergence compared with previous research results. Numerical results show that the same properties of the proposed algorithm are also effective for finding the optimal input policy due to its simplicity and fast convergence.