基于一类函数值不动点逼近的反函数迭代算法

An Iterative Formula Based on Inverse Function Iterative Algorithm of Fixed Point Approximants for Solving Nonlinear Equations

目的:函数值不动点逼近作为求解非线性方程根的一种重要算法,需要满足特定的迭代条件。方法:基于一类不动点逼近研究在不满足特定迭代条件下对一类复杂非线性方程求根。结果:提出3种基于反函数而又避免求反函数的迭代算法。结论:通过收敛性分析和数值实例证明这3种方法能有效控制重根附近发散,具有一定的实效性。

Objective:As a method for addressing the roots of nonlinear equations,the fixed point of function approximation needs to satisfy specific iteration conditions.Methods:In this paper,we study how to seek the roots of a class of complex nonlinear equations that don’t satisfy specific iteration conditions.Results:Propose three iterative algorithms based on inverse functions but without inverting functions.Conclusion:It proves that these three methods can effectively control the divergence around the repeated roots with certain effectiveness through convergence analysis and numerical examples.