Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 919-949 |
Number of pages | 31 |
Journal | BIT Numerical Mathematics |
Volume | 56 |
Issue number | 3 |
Early online date | 16 Dec 2015 |
DOIs | |
Publication status | Published - 1 Sept 2016 |
Keywords
- Arnoldi–Tikhonov method
- Discrepancy principle
- Ill-posed problems
- Multi-parameter Tikhonov method