International Open Access Journal Platform

logo
open
cover
Current Views: 33366
Current Downloads: 45462

Study on Dynamical System

ISSN Print:2707-3726
ISSN Online:2707-3734
Contact Editorial Office
Join Us
DATABASE
SUBSCRIBE
Journal index
Journal
Your email address

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 look925 look814
  • 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.
Already have an account?
+86 027-59302486