求多项式全部零点的快速Halley算法

The Fast Halley Algorithm for Finding all Zeros of a Polynomial

在Halley圆盘迭代法的基础上,用圆盘算术构造了一种求多项式全部零点的快速Halley算法,并在与Halley迭代法相同的条件下建立了它的收敛性定理,该算法取得了七阶收敛速度。数值结果表明该算法是十分有效的。

Based on the Halley circular iteration method, a fast Halley algorithm is constructed by circular arithmetic for finding all zeros of a polynomial, and the convergence has been established under the same condition as that for the Halley iteration method, the convergence rate of seventh order is obtained. The numerical experiments show the efficiency of the proposed algorithm.