Abstract and Applied Analysis
Volume 2008 (2008), Article ID 192679, 19 pages
Minimization of Tikhonov Functionals in Banach Spaces
1Center for Industrial Mathematics, University of Bremen, Bremen 28334, Germany
2Fakultät für Maschinenbau, Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Holstenhofweg 85, Hamburg 22043, Germany
Received 3 July 2007; Accepted 31 October 2007
Academic Editor: Simeon Reich
Copyright © 2008 Thomas Bonesky et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.