关于非线性方程求根的几点注记

Notes on the Solution of Nonlinear Equations in One Variable

本文给出了关于非线性方程求根的几个结果 .先给出迭代法整体收敛的一个充分条件 ,并利用它证明了牛顿法整体收敛的一个结果 ,然后讨论割线法及两个新的近似牛顿法的收敛性 。

In this paper is reported several results obtained from the solution of nonlinear equations in one variable.At first a sufficient condition for global convergence is given for the iterative method,to be used to prove a global convergence for Newton's method.Then the convergency of the secant method and of the two new methods for Newton's approximation is discussed,with numerical examples given for the latter.