二步迭代法在中心仿射Hlder条件下的收敛性  

Convergence analysis of the two-step combined method under center affine Hlder condition

作　　者：徐秀斌[1] 周文静 XU Xiubin;ZHOU Wenjing(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）》2018年第4期361-366,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(11671364; 11671365);浙江省自然科学基金资助项目(17A010006)

摘　　要：研究了Banach空间中非线性算子方程的求解问题,在一阶Fréchet导数和二阶Fréchet导数分别满足L平均中心仿射Hlder条件和L平均Lipschitz条件下,讨论了二步迭代法的局部收敛性,得到了局部收敛性的条件,同时证明了该方法的R收敛阶至少是1+p/2+(1+p)24+p2.Under the center affine H lder condition with L average and the Lipschitz condition with L average for the first and second Fr chet derivatives,respectively,the local convergence of a two-step combined method for solving nonlinear operator equations was studied.Some local convergence was given,the R order of convergence was proved to be at least 1+p[]2+(1+p)\+2[]4+p\+2 under these conditions.

关 键 词：非线性算子方程 二步迭代法 L平均中心仿射Hlder条件 局部收敛性 R收敛阶 

分 类 号：O241.7[理学—计算数学]