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 Steiglitzʹ 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 Steiglitzʹ 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.