Abstract and Applied Analysis

Minimization of Tikhonov Functionals in Banach Spaces

Thomas Bonesky, Kamil S. Kazimierski, Peter Maass, Frank Schöpfer, and Thomas Schuster

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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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Abstr. Appl. Anal., Volume 2008 (2008), Article ID 192679, 19 pages.

First available in Project Euclid: 9 September 2008

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Bonesky, Thomas; Kazimierski, Kamil S.; Maass, Peter; Schöpfer, Frank; Schuster, Thomas. Minimization of Tikhonov Functionals in Banach Spaces. Abstr. Appl. Anal. 2008 (2008), Article ID 192679, 19 pages. doi:10.1155/2008/192679. https://projecteuclid.org/euclid.aaa/1220969150

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