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2008 Minimization of Tikhonov Functionals in Banach Spaces
Thomas Bonesky, Kamil S. Kazimierski, Peter Maass, Frank Schöpfer, Thomas Schuster
Abstr. Appl. Anal. 2008: 1-19 (2008). DOI: 10.1155/2008/192679


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.


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Thomas Bonesky. Kamil S. Kazimierski. Peter Maass. Frank Schöpfer. Thomas Schuster. "Minimization of Tikhonov Functionals in Banach Spaces." Abstr. Appl. Anal. 2008 1 - 19, 2008.


Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1357.49135
MathSciNet: MR2393115
Digital Object Identifier: 10.1155/2008/192679

Rights: Copyright © 2008 Hindawi

Vol.2008 • 2008
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