中文摘要：

多项式方程求根在理论和实践中都是非常重要的问题之一，不但在应用数学而且在许多工程、物理、计算机科学、天文学、经济学等领域中也有着广泛而重要的应用．本文针对同时求解多项式方程所有单根的问题提出一簇带参数的并行高效迭代法，新方法是利用了修正的Chebyshev方法对三阶收敛的Enrlich—Aberth方法进行了加速．理论上我们证明该方法是局部收敛的，且收敛阶可以达到五阶．数值例子和效率分析都表明新方法的高效性与优越性．

英文摘要：

Solving zeros in a polynomial equation is significant both in theory and in practice. It is widely used not only in applied mathematics but also in many fields such as engineering sciences, physics, computer science, astronomy, finance, and so on. In this paper, a family of parallel iterative methods to simultaneously determine all roots of a polynomial equation is proposed. The new method is an one-parameter family of simultaneous methods to determine all distinct zeros of a polynomial, which is obtained by applying a family of third-order modified Chebyshev＇s methods to correct the Ehrlich-Aberth method. It is proved that the proposed method is locally convergent of fifth order. Some numerical results are presented to show that the new method is more efficient than some commonly used methods.