非线性方程迭代算法收敛性分析

Analysis of Convergency of Iteration Algorithm of Nonlinear Equation

从几何上分析了迭代格式xn+ 1=φ(xn)所产生的序列收敛于方程根的收敛条件 ,导出了不依赖函数可导性判断迭代序列收敛的收敛定理 ,给出了产生收敛的迭代序列的技巧。

This paper geometrically analyses the convergence condition by which the sequence brought by the iteration formula x n+1 =φ(x n) converges to the root of equation x=φ(x) , educes a convergency theorem by which whether a sequence can or cannot converge to the root of the equation can be judged without considering derivability of φ(x) , and gives some techniques of iterative algorithm.