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- Title
A new highly anti-interference regularization method for ill-posed problems.
- Authors
Hai Liang Zhuang; Hai Bo Chen
- Abstract
The solution of inverse problems has many applications in mathematical physics. Regularization methods can be applied to obtain the solution of ill-conditioned inverse problems by solving a family of neighboring well-posed problems. Thus, it is significant to investigate the regularization methods to increase the accuracy and efficiency of the solution of inverse problems. In this work, a new regularization filter and the related regularization method based on the singular system theory of compact operator are proposed to solve ill-posed problems. The Cauchy problem of Laplace equation of the first kind is a kind of well-known ill-posed problem. Numerical tests show that the proposed regularization method can solve the Cauchy problems more efficiently under a proper selection of regularization parameters. Numerical results also show that the proposed method is especially effective in solving ill-posed problems with big perturbations.
- Subjects
INVERSE problems; MATHEMATICAL regularization; MATHEMATICAL optimization; PARTIAL differential equations; ARTIFICIAL intelligence
- Publication
Vibroengineering Procedia, 2017, Vol 15, p128
- ISSN
2345-0533
- Publication type
Article
- DOI
10.21595/vp.2017.19358