一簇同时求代数方程根的双参数加速方法(英文)

A Family of Two-parameters Accelerated Zero-finding Methods for Algebraic Equation

无论在理论上还是在实践中,求解多项式方程的零点都是非常重要的,这个问题不仅在应用数学而且在许多领域,如工程、天文学、经济学等领域中也有着广泛而重要的应用.本文应用修正的Newton方法校正Enrlich-Aberth型方法,提出了一簇具有双参数的并行迭代法.新方法能同时求出代数方程的所有单根.我们证明了新方法是局部收敛的,且收敛阶可以达到4阶,并呈现出比一些常用方法更好的效率与优势.

Solving zeros to a polynomial equation is significant in both theory and practice. It is widely used not only in applied mathematics but also in many fields such as engineering sciences, astronomy, finance, and so on. In this paper, by applying the modified Newton method to improve the Enrlich-Aberth type algorithm, a new par- allel iterative scheme, including two parameters, is designed to compute all distinct roots of an algebraic equation simultaneously. The new scheme is shown to admit fourth-order convergency locally, and exhibits good efficiency compared with other common methods.