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The Sources Reconstruction Method (SRM) is an integral-equation based technique for antenna diagnostics and Near Field-to-Far Field transformation. SRM characteristics make possible the application of acceleration schemes in order to speed-up the calculation of the equivalent currents given the radiated fields. This work introduces the Adaptive Cross Approximation algorithm (ACA) combined with an iterative solver (Conjugate Gradient method, CG), with the aim of reducing the computational cost of the SRM. An application example in which the proposed CG-ACA is compared with conventional CG solution is included in the paper.