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正则化方法求解反问题中的算子方程 Au=f

Solving Unbounded Linear Operators with regularization method

Study on Dynamical System / 2019,1(1): 1-10 / 2019-12-18 926 815

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• Authors: 郭玲     
• Information:

  东莞市电子科技学校学校，东莞

• Keywords: 反间题；动力系统方法；正则化；半群
• inverse problem; dynamical system method; regularization; semigroup
• Abstract: 针对反问题中出现的第一类算子方程 Au=f，其中 A 是实 Hilbert 空间 H上的一个无界线性算子。利用动力系统方法和正则化方法，求解上述问题的正则化问题的解：u' (t)=-A*(Au(t)-f)利用线性算子半群理论可以得到上述正则化问题的解的半群表示，并证明了当t ↑∞时，所得的正则化解收敛于原问题的解。
• for the first kind of operator equation Au = f, a is an unbounded linear operator on the real Hilbert space H. The dynamic system method and regularization method are used to solve the regularization problems of the above problems u' (t)=-A*(Au(t)-f) By using the theory of linear operator semigroup, we can obtain the semigroup representation of the solution of the above-mentioned regularization problem, and prove that when t ↑ ∞, the regularization solution obtained converges to the solution of the original problem.
• DOI: https://doi.org/10.35534/sds.0101001c
• Cite: 郭玲．正则化方法求解反问题中的算子方程 Au=f［J］．动力系统研究，2019，1（1）：1-10．