ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Image Restoration and Reconstruction

Thu 16:00–16:30, Room AV 01.12
Iterated Tikhonov Regularization with a General Penalty Term
Lothar Reichel (Kent State University)
Joint work with Alessandro Buccini (Universitá dell'Insubria); Marco Donatelli (Universitá dell'Insubria); Guangxin Huang (Geomathematics Key Laboratory of Sichuan); Feng Yin (Geomathematics Key Laboratory of Sichuan)

Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. We discuss convergence properties of iterated Tikhonov regularization with a regularization matrix different from the identity. Computed examples illustrate the competitiveness of this method.