Greedy Tikhonov regularization for large linear ill-posed problems

Authors:
L. Reichel;H. Sadok;A. Shyshkov
Affiliations:
Department of Mathematical Sciences, Kent State University, Kent, OH, USA;Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral, Centre Universtaire de la Mi-Voix, Calais cedex, France;Department of Mathematical Sciences, Kent State University, Kent, OH, USA
Venue:
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Year:
2007

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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.