关于一种Weierstrass型根寻找方法族的加速收敛性
On a family of Weierstrass-type root-finding methods with accelerated convergence
AI总结：
本文研究了一种Weierstrass型迭代方法族，提出在可计算的初始条件下和后验误差估计下，该方法族的半局部收敛性结果。
摘要：
Kyurkchiev和Andreev（1985）构造了一个无限序列的Weierstrass型迭代方法，用于同时近似多项式的所有零点。该序列的第一个成员是著名的Weierstrass方法（1891），第二个是Nourein方法（1977）。对于给定的整数$N \ge 1$，该族的第$N$个方法具有收敛阶$N+1$。目前文献中仅有关于这些方法的局部收敛性结果。本文的主要目的是在可计算的初始条件下和可计算的后验误差估计下，为Weierstrass型方法提供半局部收敛性结果。
英文摘要：
Kyurkchiev and Andreev (1985) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of this sequence of iterative methods is the famous method of Weierstrass (1891) and the second one is the method of Nourein (1977). For a given integer $N \ge 1$, the $N$th method of this family has the order of convergence ${N+1}$. Currently in the literature, there are only local convergence results for these methods. The main purpose of this paper is to present semilocal convergence results for the Weierstrass-type methods under computationally verifiable initial conditions and with computationally verifiable a posteriori error estimates.
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