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不可微非线性方程的修正牛顿迭代法的收敛性分析

Analysis of convergence of a modified Newton′s method for solving nondifferentiable equations
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摘要 在求解非线性算子方程F(x)=0时,若导数不存在,则可用修正牛顿法代替牛顿法进行迭代,并用优函数的方法证明了它的收敛性,从而给出了收敛性判断的条件、收敛性证明及迭代法收敛球半径和方程具有唯一解的球的半径估计,并由此得到了几个推论.主要定理推广了相关文献的结果. It was studied about solving nonlinear operator equation F（x） = 0, when the derivative of operator did not exist. A modified Newton iterative method and majorant function were introduced to discuss the convergence, the condition of convergence, the solution of equation and the radius of convergence ball, and several inferences. Specifically, the main theorem obtained in related literatures were extended.
作者 金皓苹 徐秀斌
机构地区 浙江师范大学数理与信息工程学院
出处 《浙江师范大学学报（自然科学版）》 CAS 2012年第1期5-10,共6页 Journal of Zhejiang Normal University:Natural Sciences
关键词 非线性算子方程 修正牛顿迭代法 收敛半径 不可微 优序列 nonlinear operator equation modification of Newton＇s iteration method convergence radius nondifferentiable the majorant sequence
分类号 O241 [理学—计算数学]
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参考文献9

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浙江师范大学学报（自然科学版）
2012年 第1期

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