【摘要】 研究了具有不可微算子非线性方程的求解问题,讨论了一个二步迭代法的半局部收敛性,引进了一类弱ω条件.具体地说,当非线性算子F的一阶导数和非线性算子G的一阶差商满足ω条件时,证明了该方法的半局部收敛定理,同时得到了解的唯一性定理,从而推广了非线性算子F的一阶导数和非线性算子G的一阶差商满足Lipschitz条件下的一个已有结果.最后,用数值例子说明了该方法的合理性.更多还原

【Abstract】 The semilocal convergence of a two-step iteration method for solving nonlinear equations with nondifferentiable operators was studied. Some weak ω conditions were proposed. Specifically, when the first derivative of the nonlinear operator F and the first difference quotient of the nonlinear operator G satisfied the ω conditions, the semilocal convergence theorem and the uniqueness theorem of solutions were obtained, thus, some known results in a previous published paper, where the first derivative of the nonlinear operator F and the first difference quotient of the nonlinear operator G satisfied Lipschitz condition, were generalized. Finally, a numerical example was given to demonstrate the rationality of the method.更多还原