Easy partial fraction expansion with multiple poles

Karni, S.

doi:10.1109/proc.1969.6934

Cited by 23 publications

(3 citation statements)

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“…This is Brugia's main result; more details can be found in [4]. Equations (5) and (6) can generate a linear system of equations and then Gramer's method can used to solve the equations to obtain the derivatives of ( ). It represents a very efficient pfe method and the computer implementation is easier to be accomplished compared with many other existing "tricky" methods.…”

Section: Computing Residues Of Factorized Functions Brugia [4]mentioning

confidence: 94%

“…This is Linnér's main result. In the method, the derivatives of ( ) are calculated using equations like (5) and (6) and it also requires ̸ = and ̸ = , which can cause inconvenience in practice. In the following part, we first show how to extend to zeros and poles of ( ).…”

Section: Computing Residual Polynomial Coefficients Of Factorizedmentioning

confidence: 99%

“…Most of existing methods assume that the rational function is written in expanded form. In [6], Karni proposed an algebraic procedure for pfe. Karni's algorithm, unfortunately, is limited to just those cases where the degree of the numerator is no more than the number of poles.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions

Wang

2014

Journal of Applied Mathematics

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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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Section: Computing Residues Of Factorized Functions Brugia [4]mentioning

confidence: 94%

Section: Computing Residual Polynomial Coefficients Of Factorizedmentioning

confidence: 99%