Newton-Steffensen型迭代在广义Lipschitz条件下的半局部收敛性  

On semilocal convergence for the Newton-Steffensen method under generalized Lipschitz conditions

作　　者：陆东 梁娟 何育宇 凌永辉 LU Dong;LIANG Juan;HE Yuyu;LING Yonghui(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2020年第4期15-21,共7页Journal of Minnan Normal University：Natural Science

基　　金：福建省中青年教师教育资助项目(JT180300);福建省自然科学基金资助项目(2016J05015)。

摘　　要：研究了一种Newton-Steffensen型迭代法求解Banach空间中非线性算子方程的半局部收敛问题.当非线性算子F的一阶导数满足广义Lipschitz条件时,得到了Newton-Steffensen法的三阶收敛性.所得结果推广了相关文献的结果.The present paper concerns with the semilocal convergence problems for a Newton-Steffensen iterative method in Banach spaces.When the Fréchet derivative of the nonlinear operator F satisfies a generalized Lipschitz condition,a new semilocal convergence result is obtained for the Newton-Steffensen method.Our result extends the corresponding results in existing works.

关 键 词：Newton-Steffensen 广义Lipschitz条件 半局部收敛 

分 类 号：O241.82[理学—计算数学]