Preconditioning Landweber iteration in Hilbert scales

  title={Preconditioning Landweber iteration in Hilbert scales},
  author={Herbert Egger and Andreas Neubauer},
  journal={Numerische Mathematik},
In this paper we investigate convergence of Landweber iteration in Hilbert scales for linear and nonlinear inverse problems. As opposed to the usual application of Hilbert scales in the framework of regularization methods, we focus here on the case s ≤ 0, which (for Tikhonov regularization) corresponds to regularization in a weaker norm. In this case, the Hilbert scale operator L−2s appearing in the iteration acts as a preconditioner, which significantly reduces the number of iterations needed… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 13 references

A convergence analysis of the Landweber iteration for nonlinear ill-posed problems

  • M. Hanke, A. Neubauer, O. Scherzer
  • Numer. Math., 72:21–37
  • 1995
Highly Influential
4 Excerpts

Error estimates for regularization methods in Hilbert scales

  • U. Tautenhahn
  • SIAM J. Numer. Anal., 33:2120–2130
  • 1996
2 Excerpts

Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales

  • A. Neubauer
  • Appl. Anal., 46:59–72
  • 1992
2 Excerpts

Accelerated Landweber iterations for the solution of ill-posed equations

  • M. Hanke
  • Numer. Math., 60:341–373
  • 1991
1 Excerpt

Error bounds for Tikhonov regularization in Hilbert scales

  • F. Natterer
  • Appl. Anal., 18:29–37
  • 1984
2 Excerpts

The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind

  • C. W. Groetsch
  • Pitman, Boston
  • 1984
1 Excerpt

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