Symbolic-numeric computation of Wu's method using stabilizing algorithm

Kei-ichi Shiraishi
siraisi@dc.takuma-ct.ac.jp
Dept of Control Engineering
Takuma National College of Technology
551 Kohda, Takuma-cho, Mitoyo-gun
Japan

Hiroshi Kai
kai@cs.ehime-u.ac.jp
Department of Computer Science
Ehime University
Bunkyo-cho 3
Japan

Matu-Tarow Noda
noda@cs.ehime-u.ac.jp
Department of Computer Science
Ehime University
Bunkyo-cho 3
Japan

Abstract

We have proposed that two types of symbolic-numeric combined methods to solve polynomial equations by using Ritt-Wu's characteristic sets method. In this paper, we consider to make the methods to be faster, or to parallelize. One of the methods uses stabilizing algorithm proposed by Shirayanagi and Sweedler. In the algorithm, Wu's method is combined with a numeric computation carefully, results may be accurate and stable, and furthermore computations may be done quickly. Furthermore, we consider parallelization of the stabilizing algorithm of Wu's method.


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