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Abstract
A demonstration is made of the analogy between the method of superresolution proposed by Gerchberg, and the iterative resolution of linear systems by the Jacobi method with constraints. Using this similarity, we propose to improve the speed of convergence using other methods of linear system resolution like the relaxation Jacobi method, or the conjugate gradient method. A factor of 5000 in the number of iterations to obtain a given accuracy, was gained in a practical case, using the conjugate gradient method.