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Minimization of Tikhonov Functionals in Banach Spaces
Journal article published in 2008 by
Thomas Bonesky,
Schuster Thomas,
Peter Maass 
,
Kamil S. Kazimierski,
Frank Schöpfer
,
Kamil S. Kazimierski,
Frank Schöpfer
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.