The paper explores the numerical stability and the computational efficiency of a direct method for unfolding the resolution function from the measurements of the neutron induced reactions. A detailed resolution function formalism is laid out, followed by an overview of challenges present in a practical implementation of the method. A special matrix storage scheme is developed in order to facilitate both the memory management of the resolution function matrix, and to increase the computational efficiency of the matrix multiplication and decomposition procedures. Due to its admirable computational properties, a Cholesky decomposition is at the heart of the unfolding procedure. With the smallest but necessary modification of the matrix to be decomposed, the method is successfully applied to system of $10^5times10^5$. However, the amplification of the uncertainties during the direct inversion procedures limits the applicability of the method to high-precision measurements of neutron induced reactions.
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