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A method is presented as an ancillary to the method of moments in computing the singularity expansion description of the transient response of a scatterer. The method is based on the variational character of a generalized Rayleigh quotient. The Rayleigh quotient approximation to the matrix eigenvalue which vanishes at a pole provides an alternative to the determinant as the objective of a zero search algorithm. The alternative is more economical to compute. It is necessary to have an estimate of the correct pole location in order to initiate the Rayleigh quotient procedure. Results of computational examples and suggestions of various ways through which one may estimate the pole location are presented.