文章基本信息

标题：On the Regularization Method for Solving Ill-Posed Problems with Unbounded Operators
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作者：Nguyen Van Kinh
期刊名称：Open Journal of Optimization
印刷版ISSN：2325-7105
电子版ISSN：2325-7091
出版年度：2022
卷号：11
期号：2
页码：7-14
DOI：10.4236/ojop.2022.112002
语种：English
出版社：Scientific Research Publishing
摘要：Let be a linear, closed, and densely defined unbounded operator, where X and Y are Hilbert spaces. Assume that A is not boundedly invertible. Suppose the equation Au=f is solvable, and instead of knowing exactly f only know its approximation satisfies the condition: In this paper, we are interested a regularization method to solve the approximation solution of this equation. This approximation is a unique global minimizer of the functional , for any , defined as follows: . We also study the stability of this method when the regularization parameter is selected a priori and a posteriori. At the same time, we give an application of this method to the weak derivative operator equation in Hilbert space.
关键词：Ill-Posed ProblemRegularization MethodUnbounded Linear Operator