关于一类具有大范围收敛性的迭代法 |
| |
引用本文: | 徐利治,朱自强.关于一类具有大范围收敛性的迭代法[J].计算数学,1979,1(1):82-90. |
| |
作者姓名: | 徐利治 朱自强 |
| |
作者单位: | 吉林大学数学系,吉林大学数学系 |
| |
摘 要: | 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 |
| |
Institution: | Hsu Li-chieh Chu Tze-chiang (Mathematics Depariment, Kirin University) |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 CNKI 等数据库收录! |
| 点击此处可从《计算数学》浏览原始摘要信息 |
| 点击此处可从《计算数学》下载免费的PDF全文 |
|