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

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.