Multidirectional Subspace Expansion for One-Parameter and Multiparameter Tikhonov Regularization
详细信息 查看全文
- 作者：Ian N. Zwaan ; Michiel E. Hochstenbach
- 关键词：Tikhonov ; Multiparameter Tikhonov ; Generalized Krylov ; Multidirectional subspace expansion ; Subspace truncation ; Subspace method ; Linear discrete ill ; posed problem ; Regularization ; Regularization parameter
- 刊名：Journal of Scientific Computing
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：70
- 期：3
- 页码：990-1009
- 全文大小：732KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
- 出版者：Springer US
- ISSN：1573-7691
- 卷排序：70
文摘
Tikhonov regularization is a popular method to approximate solutions of linear discrete ill-posed problems when the observed or measured data is contaminated by noise. Multiparameter Tikhonov regularization may improve the quality of the computed approximate solutions. We propose a new iterative method for large-scale multiparameter Tikhonov regularization with general regularization operators based on a multidirectional subspace expansion. The multidirectional subspace expansion may be combined with subspace truncation to avoid excessive growth of the search space. Furthermore, we introduce a simple and effective parameter selection strategy based on the discrepancy principle and related to perturbation results.