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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Partial fraction evaluation and incomplete decomposition of a rational function whose denominator contains a repeated polynomial factor
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by J. F. Mahoney PDF
Math. Comp. 44 (1985), 167-175 Request permission

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.
References
  • Peter Henrici, Applied and computational complex analysis, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Volume 1: Power series—integration—conformal mapping—location of zeros. MR 0372162
  • Peter 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). MR 301895, DOI 10.1007/BF01587772
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 44 (1985), 167-175
  • MSC: Primary 65F99
  • DOI: https://doi.org/10.1090/S0025-5718-1985-0771038-X
  • MathSciNet review: 771038