Partial fraction evaluation and incomplete decomposition of a rational function whose denominator contains a repeated polynomial factor

Author:
J. F. Mahoney

Journal:
Math. Comp. **44** (1985), 167-175

MSC:
Primary 65F99

DOI:
https://doi.org/10.1090/S0025-5718-1985-0771038-X

MathSciNet review:
771038

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Abstract: Attention is directed to those proper rational functions whose denominators may be expressed as the product of an *N*th degree polynomial raised to the *K*th power and another polynomial of degree *M*. A method is presented for decomposing such a rational function into the sum of the *K* partial fraction terms which proceed from the repeated polynomial plus a proper rational function which completes the equality. Use is made of an extended version of Horner's scheme. Two numerical examples and an operations count are presented. The method is free of complex arithmetic provided that all of the coefficients of the entering polynomials are real.

**[1]**P. Henrici,*Applied and Computational Complex Analysis*, Vol. 1, Wiley, New York, 1974. MR**0372162 (51:8378)****[2]**P. Henrici, "An algorithm for the incomplete decomposition of a rational function into partial fractions,"*Z. Angew. Math. Phys.*, v. 22, 1971, pp. 751-755. MR**0301895 (46:1050)**

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0771038-X

Article copyright:
© Copyright 1985
American Mathematical Society