Partial-fraction expansion: part 3 [rational function numerical analysis]

This series of articles has been discussing means of obtaining partial-fraction expansions (PFEs) of rational functions numerically. In parts 1 and 2 we presented the background on Chin and Steiglitz´ algorithm (IEEE Trans. Circuits Syst., pp.42-45, 1977) for determining the PFE coefficients associated with the proper rational function H(s), which may contain multiple poles. We now continue with Chin and Steiglitz´ algorithm, laying out the particulars of forming the PFE coefficients. The analysis leads to a very straightforward algorithm that requires only a few lines of code to implement.