ω-条件下Ulm-type方法的局部收敛性  

LOCAL CONVERGENCE OF THE ULM-TYPE METHOD UNDER THE ω-CONDITION

作　　者：沈卫平 徐丽华 Shen Weiping;Xu Lihua(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004)

机构地区：[1]浙江师范大学数学与计算机科学学院,金华321004

出　　处：《高等学校计算数学学报》2020年第1期48-63,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：浙江省自然科学基金(LY17A010006).

摘　　要：由于牛顿法具有重要的理论基础和广泛的应用背景,它的收敛性得到了广泛研究([2,3,4,13,20,21,22,23]).—般而言,牛顿法的收敛性可以分成三类.一类是局部收敛性:已知方程(1)的解存在,初始点x0在该解的某个领域内时讨论牛顿法的收敛性([21,22,23]).This paper is concerned with the local convergence of the Ulm-type method for solving nonlinear operator equations,which can avoid solving(approximate) Jacobian equations.Under the assumption that the Frechet derivative satisfies the ω-condition,we establish a superlinear convergence of the Ulm-type method.Moreover,the radius of the convergent ball is also estimated.Some numerical experiments are provided to illustrate the theoretical results.

关 键 词：局部收敛性 牛顿法 初始点 

分 类 号：O241.7[理学—计算数学]