Title :
An Algorithm for the Machine Computation of Partial-Fractions Expansion of Functions Having Multiple Poles
Author :
Godbole, Sadashiva S.
Abstract :
The partial-fractions expansion of a function F(s)/(s-a)m, m > 1, involves the computation of m coefficients, namely (1 /i!)(diF(a)/dsi), 0 ≤ i ≤ m-1. Wehrhahn [1] and Karni [3] have provided a method for computing these coefficients algebraically. A new approach is taken here which involves approximating a multiple pole by neighboring simple poles. The theory developed turns out to have a very interesting resemblance to the FFT algorithm. The algorithm is illustrated by several examples. Typical applications are finding the inverse Laplace transform of a function having multiple poles and the evaluation of higher order derivatives of an arbitrary function H(z) at some arbitrary z=z0.
Keywords :
Discrete Fourier transform (DFT), fast Fourier transform (FFT), multiple pole, partial-fractions expansion.; Discrete Fourier transforms; Distributed computing; Fast Fourier transforms; Fourier transforms; Laplace equations; Taylor series; Discrete Fourier transform (DFT), fast Fourier transform (FFT), multiple pole, partial-fractions expansion.;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/T-C.1971.223099