基于函数值不动点逼近的四类改进迭代算法  

An Iterative Formula Based on Improvement of Fixed Point Approximants for Solving Nonlinear Equations

作　　者：郭巧 杨兵[2] 吴昌广 GUO Qiao;YANG Bing;WU Chang-guang(School of Computer and Information Technology,Anhui Vocational and TechnicalCollege,Hefei 230611,China;School of Intelligent Manufacturing,Anhui Vocational and Technical College,Hefei 230611,China;School of Computer and Information Engineering,Nanjing University of Scienceand Technology,Nanjing 210094,China)

机构地区：[1]安徽职业技术学院计算机与信息技术学院,安徽合肥230611 [2]安徽职业技术学院智能制造学院,安徽合肥230611 [3]南京理工大学计算机学院,江苏南京210094

出　　处：《长春师范大学学报》2023年第6期24-30,共7页Journal of Changchun Normal University

基　　金：2022年度职业院校数字化转型行动研究课题“职教本科背景下高等数学在新工科专业数字化教学实践改革的创新研究”(KT22086);2022年度职业院校数字化转型行动研究课题“模具设计与制造专业数字化转型与产教融合实践研究”(KT22223);2020年度安徽省教育厅教学示范课“冲压成形工艺与模具设计”(2020SJJXSFK1415)。

摘　　要：基于函数值不动点逼近是求解非线性方程简单迭代的一个重要方面.本文通过对不动点迭代的分析,构造四类改进的迭代算法,并通过对迭代公式的收敛性分析和数值计算,证明四类改进迭代算法的收敛速度明显优于简单迭代,并能够有效控制发散,算法具有一定的理论和实用价值.Fixed point approximation is an important aspect of rational approximation.The paper presents four improvement iterative algorithms for solving nonlinear equations by using fixed point approximants,and through the convergence of the iterative algorithms and numerical calculation to show that the new formulas have higher convergence speed than the fixed point iterative formula and avoid divergence near the double root.It has better practical value and stability.

关 键 词：不动点迭代 非线性方程 逼近 迭代算法 

分 类 号：O241.7[理学—计算数学]