The Derivation of Two Parallel Zero-Finding Algorithms of Polynomials

Abstract

本文研究適合平行計算之二種演算法Weierstrass法及Aberth法以求解多項式之零位。我們說明由函數疊代分析可以導出此二種演算法。同時也驗證Weierstrass法可由不動點疊代法結合隱式除法計算導出，而牛頓法結合隱式除法可以計算出Aberth法。

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.