非线性方程求根的一类预测-校正迭代方法  

A Class of Prediction-correction Iterative Methods for Finding Root of a Nonlinear Equation

作　　者：于爽 王梓宽 YU Shuang;WANG Zi-kuan(Institute of Science and Engineering Computing, School of Science, East China University of Technology, Nanchang 330013, China;Qianhu School, Nanchang University, Nanchang 330031, China)

机构地区：[1]东华理工大学理学院科学与工程计算研究所,江西南昌330013 [2]南昌大学前湖学院,江西南昌330031

出　　处：《数学的实践与认识》2019年第12期300-306,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11861007);江西省主要学科学术与技术带头人资助计划(2017zBcB22019);江西省教育厅科技计划(GJJ170444);东华理工大学研究生创新项目(DHYC-201830)

摘　　要：考虑了非线性方程求根问题,即从一类特殊的积分出发获得了非线性方程求根的方法,所得方法推广了已有结果.将所得方法与变形的牛顿迭代法相结合,获得了非线性方程求根的实用的预测-校正格式,并证明了当β=1/2时格式至少具有局部平方收敛.数值算例表明,所得格式迭代步数少,收敛速度快,是非线性方程求根的有效方法之一.In this paper,the root problem of nonlinear equations is considered.A class of methods for finding the root of a nonlinear equation are obtained from a special kind of integral.The obtained methods generalize the existing results.By combing the obtained methods with the modified Newton iterative method,the practical prediction-correction schemes are proposed for finding the root of a nonlinear equation;and it is proved that these schemes have at least local square convergence when β=1/2.Numerical examples show that the number of iteration steps of the practical prediction-correction schemes is small and the corresponding convergence speed is fast.Therefore,the practical prediction-correction schemes are effective for finding root of a nonlinear equation.

关 键 词：方程求根 非线性 迭代方法 校正 预测 牛顿迭代法 数值算例 平方收敛 

分 类 号：O175[理学—数学]