Abstract and Applied Analysis
Volume 2008 (2008), Article ID 192679, 19 pages
doi:10.1155/2008/192679
Minimization of Tikhonov functionals in Banach spaces
Thomas Bonesky1
, Kamil S. Kazimierski1
, Peter Maass1
, Frank Schöpfer4
and Thomas Schuster4
1Center for Industrial Mathematics, University of Bremen, Bremen 28334, Germany
4Fakultät für Maschinenbau, Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Holstenhofweg 85, Hamburg 22043, Germany
Abstract
Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest descent method, whereby the iterations are directly carried out in the underlying space, and the other one performs iterations in the dual space. We prove strong convergence of both methods.