方程求根迭代法的一类修正格式与收敛性分析

A Class of Modified Schemes and Convergence Analysis for the Iterative Method for Solving Equation

研究方程求根迭代法的一类修正格式及其收敛性.通过引入乘子函数λ和利用泰勒展开式,建立一般迭代法的修正格式,并对其进行收敛性分析,进而给出修正格式的全局收敛和局部收敛条件;通过误差补偿,建立修正格式的加速公式,以保证在较高精度的情况下降低一般迭代公式对初值选择的敏感度.

In this paper,we study a class of modified schemes and convergence of iterative methods for solving equations.Firstly,by introducing the multiplier functionλand using the Taylor expansion,the modified format of the general iterative method is established and its convergence is analyzed.The conditions of the global convergence and local convergence of the modified scheme are given.On this basis,through error compensation,the acceleration formula of the modified iterative method is obtained to ensure that the sensitivity of the general iterative formula to the initial value selection is reduced with high accuracy.