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Minimization of Tikhonov Functionals in Banach Spaces

Author

Listed:
  • Thomas Bonesky
  • Kamil S. Kazimierski
  • Peter Maass
  • Frank Schöpfer
  • Thomas Schuster

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.

Suggested Citation

  • Thomas Bonesky & Kamil S. Kazimierski & Peter Maass & Frank Schöpfer & Thomas Schuster, 2008. "Minimization of Tikhonov Functionals in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-19, March.
    • Handle: RePEc:hin:jnlaaa:192679
    DOI: 10.1155/2008/192679
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