Holder条件下一种Newton类方法的半局部收敛性

Semilocal convergence of a Newton-like method under Holder condition

从Kantorovich理论出发,研究了不可微非线性算子的求解问题,探讨了一种Newton类方法的半局部收敛性.在算子可微部分一阶导数满足Holder条件、不可微部分满足Lipschitz条件下,通过构造优函数,利用优序列证明了方法的半局部收敛定理,同时也给出了解的唯一性.

Using Kantorovich′s theory,the semilocal convergence of a Newton-like method for solving nondifferential operator equation was studied.Under the assumptions that the first derivative of the differential part satisfied Holder condition and the nondifferential part satisfied Lipschitz condition,by constructing majorizing function and majorizing sequence,the semilocal convergence theorem was proved,moreover,the uniqueness of solution was presented.