Fast Algorithms for Partial Fraction Decomposition
Hsiang-Tsung Kung,D. M. Tong +1 more
TL;DR: The partial fraction decomposition of a proper rational function whose denominator has degree n and is given in general factored form can be done in O(n \log^{2}n) operations in the worst case.
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Abstract: The partial fraction decomposition of a proper rational function whose denominator has degree n and is given in general factored form can be done in $O(n \log^{2}n)$ operations in the worst case. Previous algorithms require $O(n^{3})$ operations, and $O(n \log^{2}n)$ operations for the special case where the factors appearing in the denominator are all linear.
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Citations
Factorization of Polynomials
E. Kaltofen
- 01 Jan 1983
TL;DR: Algorithms for factoring polynomials in one or more variables over various coefficient domains are discussed and an attempt is made to establish a complete historic trace for today’s methods.
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Filtering, Prediction and Simulation Methods for Noncausal Processes
TL;DR: In this article, a closed-form functional estimator of the predictive density for noncausal and mixed processes is introduced that provides prediction intervals up to a finite horizon H. The authors also propose a recursive BHHH algorithm for the maximization of the approximate loglikelihood function, which calculates the filtered values of the unobserved causal and non-causal components of the process.
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Computing with polynomials given by straight-line programs II sparse factorization
Erich Kaltofen
- 21 Oct 1985
TL;DR: An algorithm for the factorization of a multivariate polynomial represented by a straight-line program into its irreducible factors represented as sparse polynomials is developed with controllably high probability the correct factorization.
37
On the complexity of factoring polynomials with integer coefficients
Erich Kaltofen
- 01 Jan 1982
TL;DR: The evaluation process leads to the study of the Hilbert irreducibility theorem, an effective version of which provides us with an alternate polynomial time reduction from multivariate to bivariate polynomials factorization and irreduceibility testing.
25
Algebraic algorithms using p-adic constructions
David Y. Y. Yun
- 10 Aug 1976
TL;DR: Whatever the field currently known as symbolic and algebraic manipulation, the most fundamental part of any symbolic computer software system for the actual computing is always the workhorse subpackage that deals with polynomial and rational functions.
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Gaussian elimination is not optimal
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