求解非线性算子方程的两步组合方法的收敛性分析
Convergence Analysis of the Two-Step Combined Method for Solving Nonlinear Operator Equations
DOI: 10.12677/AAM.2017.61011, PDF, HTML, XML, 下载: 1,660  浏览: 4,252  科研立项经费支持
作者: 吴伟笛, 沈卫平, 徐丽华：浙江师范大学数学系，浙江 金华
关键词: 半局部收敛性；两步组合方法；差商；Semi-Local Convergence； Two-Step Combined Method； Divided Differences
摘要: 本文考虑求解非线性方程问题的两步组合方法的收敛性。在某些连续性条件下，我们给出了该方法的半局部收敛性。另外对算子方程的解的唯一性也做出了说明。最后通过数值例子来说明收敛性分析的有效性。
Abstract: In this paper, we consider the convergence of the two-step combined method for solving nonlinear operator equations. A semi-local convergence of the method is presented under some continuity conditions. Moreover, we establish the uniqueness result of the solutions. Finally, a numerical example is provided to demonstrate our theoretical results.
文章引用：吴伟笛, 沈卫平, 徐丽华. 求解非线性算子方程的两步组合方法的收敛性分析[J]. 应用数学进展, 2017, 6(1): 90-103. http://dx.doi.org/10.12677/AAM.2017.61011

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