关于Ehrlich迭代法的一种推广

On a Generalization of Ehrlich′s Method

讨论Ehrlich迭代法的一种推广形式,给出收敛性定理及其简洁证明,并比较它和Newton迭代法的计算效率,得出当多项式的根全为单根时若多项式次数不低于4,则Ehrlich迭代法的效率高于Newton迭代法;当多项式的根不全为单根时,则Ehrlich迭代法的效率总高于Newton迭代法。

A generalized Ehrlich＇s method is discussed; a version of its convergence theorem is proposed and a more concise proof of the theorem is given. Finally, the numerical efficiency of the generalized Ehrlichrs method and that of Newton method are compared. It is concluded that the Ehrlich＇s method is more efficient than Newton method for polynomials of degree n≥4 with simple roots and for all polynomials with multiple roots.