Recursive formulas for the partial fraction expansion of a rational function with multiple poles

1973 ◽  
Vol 61 (8) ◽  
pp. 1139-1140 ◽  
Author(s):  
Feng-Cheng Chang
Keyword(s):  
Rational Function ◽  
Partial Fraction ◽  
Partial Fraction Expansion ◽  
Recursive Formulas ◽  
Multiple Poles

An Algorithm for Partial-Fraction Expansion

1972 ◽  
Vol 65 (3) ◽  
pp. 237-239
Author(s):  
Joseph W. Rogers ◽  
Margaret Anne Rogers
Keyword(s):  
Rational Function ◽  
Partial Fraction ◽  
Partial Fraction Expansion ◽  
Partial Fractions

We Usually expand a rational function by first reducing it to the sum of a polynomial and a proper fraction that is the quotient of two polynomials in which the degree of the numerator is less than the degree of the denominator. We expand the fraction by writing it as a sum of partial fractions with undetermined numerator coefficients.

scholarly journals Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Youneng Ma ◽  
Jinhua Yu ◽  
Yuanyuan Wang
Keyword(s):  
Applied Mathematics ◽  
Rational Functions ◽  
Partial Fraction ◽  
Polynomial Coefficients ◽  
Partial Fraction Expansion ◽  
Computation Process ◽  
Classic Technique ◽  
Recursive Formulas ◽  
Proper Functions ◽  
Manual Calculation

Partial fraction expansion (pfe) is a classic technique used in many fields of pure or applied mathematics. The paper focuses on the pfe of general rational functions in both factorized and expanded form. Novel, simple, and recursive formulas for the computation of residues and residual polynomial coefficients are derived. The proposed pfe methods require only simple pure-algebraic operations in the whole computation process. They do not involve derivatives when tackling proper functions and require no polynomial division when dealing with improper functions. The methods are efficient and very easy to apply for both computer and manual calculation. Various numerical experiments confirm that the proposed methods can achieve quite desirable accuracy even for pfe of rational functions with multiple high-order poles or some tricky ill-conditioned poles.

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