牛顿法在两类弱Hlder条件下的收敛性  

Convergence analysis of Newton method under two types of weak Hlder condition

作　　者：徐秀斌[1] 李凯富 XU Xiubin LI Kaifu(College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China)

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2017年第3期241-248,共8页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11671365);浙江省自然科学基金资助项目(17A010006)

摘　　要：对于Banach空间中一般的非线性方程,在一阶导数满足L平均的仿射径向Hlder条件下,讨论了经典牛顿迭代法的局部收敛性,得到了局部收敛性条件,同时证明了该方法的R收敛阶至少为1+p.在F'满足L平均的Hlder条件下,利用递推关系,给出了牛顿法的半局部收敛性定理.Under the affine radius Holder condition with L average for the first order Frechet derivative, the local convergence of classical Newton method for solving nonlinear equations was studied. Some local convergence conditions were given, the R-order of convergence was proved to be at least 1 ＋ p under those conditions. Under Holder condition with L average for the first order Frechet derivative, by the technique based on recurrence relation instead of majorant principle, the semilocal convergence theorem was established.

关 键 词：牛顿法 L平均的仿射径向Holder条件 L平均的Holder条件 局部收敛性 半局部收敛性 

分 类 号：O241.7[理学—计算数学]