Based on a theoretical analysis of the DAMAS algorithm, proposed by Brooks and Humphreys to locate and quantify acoustic sources accurately, the paper proposes an efficient method to converge faster to the same solution by implementing standard proven algorithms. We prove that when the DAMAS converges, its limit is a solution of the Covariance matrix Fitting method, and that when the solution is unique, the DAMAS algorithm converges. We analyze the properties of the solutions to this optimization problem to explain the ability of the DAMAS algorithm to recover sparse distributions of sources, even without a regularization term. A fast implementation of the Covariance Matrix Fitting problem is also proposed. Several algorithms to solve this problem are compared. From this review, it comes that the proposed method reduces drastically memory use and computational time thus allowing to address large scale problems. An application to a large-scale 3D problem using experimental data demonstrates this numerical efficiency, and simulations are used to assess the performances of source power estimation.