• Corpus ID: 117501871

A Fast Algorithm for Partial Fraction Decompositions

@article{Xin2004AFA,
  title={A Fast Algorithm for Partial Fraction Decompositions},
  author={Guoce Xin},
  journal={arXiv: Combinatorics},
  year={2004}
}
  • G. Xin
  • Published 14 August 2004
  • Mathematics
  • arXiv: Combinatorics
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the rational function. The new algorithms use less storage space, and are suitable for parallel programming. We also discuss full partial fraction decompositions. 
A Fast Algorithm for MacMahon's Partition Analysis
  • G. Xin
  • Mathematics, Computer Science
    Electron. J. Comb.
  • 2004
TLDR
The theory of iterated Laurent series and a new algorithm for partial fraction decompositions are combined to obtain a fast algorithm for MacMahon's Omega calculus, which (partially) avoids the "run-time explosion" problem when eliminating several variables.
An Efficient Representation for Large Arrays of Rational Expressions ∗
The paper describes a method of representing an n-dimensional array of rational expressions as an (n + 1)-dimensional array of scalars and shows how this representation readily supports the

References

SHOWING 1-6 OF 6 REFERENCES
Fast computation of GCDs
  • R. Moenck
  • Mathematics, Computer Science
    STOC
  • 1973
TLDR
An integer greatest common divisor (GCD) algorithm due to Schönhage is generalized to hold in all euclidean domains which possess a fast multiplication algorithm and a new faster algorithm for multivariate polynomial GCD's can be derived.
An Algorithm for Solving Second Order Linear Homogeneous Differential Equations
Generating functions and generalized Dedekind sums
  • I. Gessel
  • Mathematics, Computer Science
    Electron. J. Comb.
  • 1997
TLDR
Three methods for evaluating sums of the form $\sum_\zeta R(\zeta)$, where $R$ is a rational function and the sum is over all $n$th roots of unity $zeta$ (often with $\zeta =1$ excluded), are discussed.
The Ring of Malcev-Neumann Series and the Residue Theorem
We develop a theory of the field of double Laurent series, iterated Laurent series, and Malcev-Neumann series that applies to most constant term evaluation problems. These include (i) MacMahon's
Algorithms, 2nd Edition
Algorithms (2nd edition)