一个Weierstrass迭代修正法的收敛性分析

Analysis of the convergence of a modified Weierstrass iteration.

为了求解多项式方程 f (z) =0 ,我们在 Weierstrass迭代的基础上给出了一个同时求解该方程所有根的迭代法 ,并对其收敛性及收敛的初始条件进行了分析 ,得出其收敛的初始条件 ,它仅与迭代的初始点有关而与方程的根无关 ,同时还证明了在此初始条件下 ,该迭代是

To solve the polynomial equation f(z)=0, this paper proposes a modified Weierstrass iteration and investigates its convergence and initial condition. It proves that the convergence has order 3 under the initial condition, and that the initial condition only depends on the initial point.