By the numbers - Partial-fraction expansion: part 2

Abstract

For Part 1 see ibid., vol.5, pp.42-44 (June 2002). In Part 1 of our discussion, after describing a simple procedure for obtaining the partial-fraction expansion (PFE) of a rational function having distinct poles only, we took some precursory steps toward an elegant algorithm by Chin and Steiglitz (1977) applicable to the general case in which the proper rational function contains multiple poles. In this article we develop Chin and Steiglitz' algorithm by rewriting the rational function in a nested form and derive a code for synthetic division.