关于非线性方程的牛顿迭代格式初始值选取的注记

Notes of the Initial Value Selection for Newton Iterative Schemes of Nonlinear Equations

基于构造非线性方程的牛顿迭代格式简便和牛顿迭代格式具有收敛快的特点,在解决实际问题时,牛顿迭代格式显得尤为重要,但是,牛顿迭代格式的初始值选取具有很大的局限性.利用泰勒级数展开,对牛顿迭代格式的收敛性进行分析,从而提出改进牛顿迭代格式的初始值选取方案,并利用不同的数值算例验证牛顿迭代格式收敛区域的改进方案的可行性,同时数值算例表明该方法具有操作简单的特点.

The Newtonian iterative scheme of nonlinear equation is simplicity and fast convergence.So the Newtonian iterative scheme is very important in solving practical problems.In general,it is difficult to select the initial value.In this paper,the convergence of Newtonian iterative scheme is analyzed by Taylor series expansion,and the good method of selecting initial value is presented.The method of selecting initial value is verified with different numerical examples.And the numerical examples show that the method is simple in operation.