解非线性不适定方程的简化动力系统方法  

A SIMPLIFIED DYNAMICAL SYSTEMS METHOD FOR SOLVING NONLINEAR ILL-POSED EQUATIONS

作　　者：黄静月 罗兴钧[1] 张荣[1] Huang Jingyue;Luo Xingjun;Zhang Rong(School of Mathematics and Computer Sciences,Gannan Normal University,Ganzhou 341000)

机构地区：[1]赣南师范大学数学与计算机科学学院,赣州341000

出　　处：《高等学校计算数学学报》2022年第4期329-343,共15页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(No.11761010,12201126)。

摘　　要：1引言本文研究解非线性方程F(u)=f(1)的简化动力系统方法,其中F:H→H为实Hilbert空间H中的非线性二次Frechet可微单调算子([1]),即<F(u)-F(v),u-v>≥0,■u,v∈H,(2)其中<·,·>表示H中的内积.假设方程(1)有解.由文献[2]可知,若F为单调连续算子.A simplified dynamical systems method for solving nonlinear ill-posed operator equation F(u)=f with monotone operator F is studied in this paper.The convergence of the simplified dynamical systems method is proved under certain conditions of the operator F and the exact solution y.In addition,the convergence of the discrete simplified dynamical systems method is studied.Finally,an example is given to verify the effectiveness of the new algorithm.

关 键 词：动力系统方法 非线性方程 连续算子 FRECHET可微 单调算子 实HILBERT空间 内积 

分 类 号：O241.1[理学—计算数学]