The Derivation of Two Parallel Zero-Finding Algorithms of Polynomials

Author: Tai-Yih Tso (Department of Mathmatics, National Taiwan Normal University)

Vol.&No.：Vol. 42 (New Version)
Date：October 1997
Pages：1-6
DOI：10.6301/JNTNU.1997.42.01

Abstract：

In this paper we study the derivation of two famous algorithms for finding all zeros of a giving polynomial. These two algorithms which are the Weierstrass method and the Aberth method are highly suited for parallel computing. It is explained that both of the two algorithms can be arrived by the functional iteration analysis. We also show that the the Weierstrass method and the Aberth method can be derived by the fixed point iteration method and the Newton method, respectively, together with the implicit deflation scheme.

Keywords：parallel computing, functional iteration analysis, zeros-finding, implicit deflation

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