Abstract and Applied Analysis

Minimization of Tikhonov Functionals in Banach Spaces

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.

Article information

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

Dates
First available in Project Euclid: 9 September 2008

https://projecteuclid.org/euclid.aaa/1220969150

Digital Object Identifier
doi:10.1155/2008/192679

Mathematical Reviews number (MathSciNet)
MR2393115

Zentralblatt MATH identifier
1357.49135

Citation

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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