  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 $10^5\times10^5$.
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.
