A new framework for multi-parameter regularization
详细信息 查看全文
- 作者：Silvia Gazzola ; Lothar Reichel
- 关键词：Ill ; posed problems ; Multi ; parameter Tikhonov method ; Arnoldi–Tikhonov method ; Discrepancy principle
- 刊名：BIT Numerical Mathematics
- 出版年：2016
- 出版时间：September 2016
- 年：2016
- 卷：56
- 期：3
- 页码：919-949
- 全文大小：1,371 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Computational Mathematics and Numerical Analysis
Numeric Computing
Mathematics - 出版者：Springer Netherlands
- ISSN：1572-9125
- 卷排序：56
文摘
This paper proposes a new approach for choosing the regularization parameters in multi-parameter regularization methods when applied to approximate the solution of linear discrete ill-posed problems. We consider both direct methods, such as Tikhonov regularization with two or more regularization terms, and iterative methods based on the projection of a Tikhonov-regularized problem onto Krylov subspaces of increasing dimension. The latter methods regularize by choosing appropriate regularization terms and the dimension of the Krylov subspace. Our investigation focuses on selecting a proper set of regularization parameters that satisfies the discrepancy principle and maximizes a suitable quantity, whose size reflects the quality of the computed approximate solution. Theoretical results are shown and illustrated by numerical experiments.