Purely real arithmetic algorithms optimized for the analytical and computational evaluation of partial fraction expansions

Partial fraction expansion of transformed functions is a familiar and powerful tool for evaluating transient responses of continuous and discrete (Laplace and Z-transform) models as well as very valuable for evaluating certain classes of integrals. The standard analytical textbook techniques as well as the standard computational algorithms are adequate, but seem to leave much to be desired when compared to the new real arithmetic algorithms presented by the authors. Furthermore, most standard computational techniques break down when the transform functions have higher-order multiple poles. Discussions of computational techniques and an analytical example are used to enhance the presentation of the new algorithm