Representations and Parallel Computations for Rational Functions
1986; Society for Industrial and Applied Mathematics; Volume: 15; Issue: 2 Linguagem: Inglês
10.1137/0215030
ISSN1095-7111
Autores Tópico(s)Digital Filter Design and Implementation
ResumoRepresentations of univariate rational functions over a given base of polynomials are considered, and a fast parallel algorithm for converting from one base representation to another is given. Special cases of this conversion include the following symbolic manipulation problems: Taylor expansion, partial fraction decomposition, Chinese remainder algorithm, elementary symmetric functions, Padé approximation, and various interpolation problems. If n is the input size, then all algorithms run in parallel time $O(\log ^2 n)$ and use $n^{O(1)} $ processors. They work over an arbitrary field.
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