关于一类具有大范围收敛性的迭代法

本文由Hadamard因子分解定理出发,证明了推广的Laguerre迭代方法对求解一类超越方程具有大范围收敛性.对复根允许存在的区域作了讨论.得出了Riemann假定成立的一个必要条件.还给出了此迭代法的Algol 60程序.

ON A CLASS OF ITERATIVE PROCESSES WITH GLOBAL CONVERGENCE

This paper investigates a class of iterative processes that can be used to find the real zeros of entire functions, which by means of Landau's proof of Hadamard's theorem, has been proved to have the property of global convergence on real axis.The region where complex roots may exist is considered.A special case corresponding to an extended form of Laguerre's method is applied to Eiemann's function (?)(t), and a kind of necessary condition, capable of numerical evaluation for testing the validity of Riemann's hypothesis is obtained.In addition, the Algol 60 program of the iterative process is given.