Greedy Tikhonov regularization for large linear ill-posed problems

Abstract

Several numerical methods for the solution of large linear ill-posed problems combine Tikhonov regularization with an iterative method based on partial Lanczos bidiagonalization of the operator. This paper discusses the determination of the regularization parameter and the dimension of the Krylov subspace for this kind of method. A method that requires a Krylov subspace of minimal dimension is referred to as greedy.

Keywords:

• Discrepancy principle
• Ill-posed problem
• Inverse problem
• Lanczos bidiagonalization
• Regularization

Acknowledgements

The research of LR and AS is supported in part by an OBR Research Challenge Grant.