一阶导数满足L-平均Lipschitz条件下Newton-Steffensen法的三阶收敛性  

Cubic convergence of Newton-Steffensen’s method for operators with L-average Lipschitz continuous derivative

作　　者：庄小军 王金华[1] ZHUANG Xiao-jun;WANG Jin-hua(Zhejiang University of Technology, Hangzhou 310023, China)

机构地区：[1]浙江工业大学理学院

出　　处：《高校应用数学学报（A辑）》2019年第3期339-356,共18页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11771397);浙江省自然科学基金(LY17A010021)

摘　　要：研究了用Newton-Steffensen法求解非线性算子方程.当非线性算子F的一阶导数满足L-平均Lipschitz条件时,建立了Newton-Steffensen法的三阶收敛判据,同时也给出了收敛球半径的估计.作为应用,当F的一阶导数满足经典的Lipschitz条件时或F满足γ-条件时,建立了Newton-Steffensen法的三阶收敛判据及给出了收敛球半径的估计.从而推广了[Journal of Nonlinear and Convex Analysis,2018,19:433-460]中的相应结果.Newton-Steffensen’s method for solving nonlinear operator equations is studied.When F’satisfies the L-average Lipschitz condition,cubic convergence criteria of Newton-Steffensen’s method is established.At the same time,an estimate of the radius of convergence ball is also presented.As applications,when F’satisfies the classical Lipschitz condition or F satisfies the γ-condition,cubic convergence criteria of Newton-Steffensen’s method is established and an estimate of the radius of convergence ball is provided,which extends the corresponding results in[Journal of Nonlinear and Convex Analysis,2018,19:433-460].

关 键 词：Newton-Steffensen法 优化函数 优化序列 L-平均Lipschitz条件 收敛准则 收敛半径 

分 类 号：O241[理学—计算数学]