The Derivation of Two Parallel Zero-Finding Algorithms of Polynomials

解多項式零位之平行演算法

左台益(Tai-Yih Tso)

《師大學報：數理與科技類》 42期 (1997/10) Pp. 1-6

https://doi.org/10.6301/JNTNU.1997.42.01

摘要

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。我們說明白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計算Aberth法。

關鍵字

平行計算 ； 函數疊代分析 ； 解零位 ； 隱式除法

並列摘要

In this paper we study the derivation of two famous algorithms for finding all zeros of a giving polynomial. The 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 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

並列關鍵字

parallel computing ； functional iteration analysis ； zeros-finding ； implicit deflation