The iterative randomized stimulation and averaging (IRSA) method was proposed for recording evoked potentials when the individual responses are overlapped. The main inconvenience of IRSA is its computational cost, associated with a large number of iterations required for recovering the evoked potentials and the computation required for each iteration [involving the whole electroencephalogram (EEG)]. This article proposes a matrix-based formulation of IRSA, which is mathematically equivalent and saves computational load (because each iteration involves just a segment with the length of the response, instead of the whole EEG). Additionally, it presents an analysis of convergence that demonstrates that IRSA converges to the least-squares (LS) deconvolution. Based on the convergence analysis, some optimizations for the IRSA algorithm are proposed. Experimental results (configured for obtaining the full-range auditory evoked potentials) show the mathematical equivalence of the different IRSA implementations and the LS-deconvolution and compare the respective computational costs of these implementations under different conditions. The proposed optimizations allow the practical use of IRSA for many clinical and research applications and provide a reduction of the computational cost, very important with respect to the conventional IRSA, and moderate with respect to the LS-deconvolution. matlab/Octave implementations of the different methods are provided as supplementary material.