Tikhonov regularization based on generalized Krylov subspace methods

Authors:
Lothar Reichel;Fiorella Sgallari;Qiang Ye
Affiliations:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA;Department of Mathematics, CIRAM, University of Bologna, Via Saragozza 8, 40123 Bologna, Italy;Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

We consider Tikhonov regularization of large linear discrete ill-posed problems with a regularization operator of general form and present an iterative scheme based on a generalized Krylov subspace method. This method simultaneously reduces both the matrix of the linear discrete ill-posed problem and the regularization operator. The reduced problem so obtained may be solved, e.g., with the aid of the singular value decomposition. Also, Tikhonov regularization with several regularization operators is discussed.