Partial fraction evaluation and incomplete decomposition of a rational function whose denominator contains a repeated polynomial factor
J. F. Mahoney
Math. Comp. 44 (1985), 167-175
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Abstract: Attention is directed to those proper rational functions whose denominators may be expressed as the product of an Nth degree polynomial raised to the Kth 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.
Henrici, Applied and computational complex analysis,
Wiley-Interscience [John Wiley & Sons], New York, 1974. Volume 1: Power
series—integration—conformal mapping—location of zeros;
Pure and Applied Mathematics. MR 0372162
Henrici, An algorithm for the incomplete decomposition of a
rational function into partial fractions, Z. Angew. Math. Phys.
22 (1971), 751–755 (English, with German summary).
0301895 (46 #1050)
- P. Henrici, Applied and Computational Complex Analysis, Vol. 1, Wiley, New York, 1974. MR 0372162 (51:8378)
- 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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