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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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ISSN
1569-3945
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Volume 15, Issue 3 (Jun 2007)

Issues

Convergence analysis of an inexact iteratively regularized Gauss-Newton method under general source conditions

S. Langer
  • Institut für Numerische und Angewandte Mathematik, Georg-August-Universität, Lotzestr. 16-18, 37083 Göttingen, Germany. Email:
/ T. Hohage
  • Institut für Numerische und Angewandte Mathematik, Georg-August-Universität, Lotzestr. 16-18, 37083 Göttingen, Germany. Email:
Published Online: 2007-06-25 | DOI: https://doi.org/10.1515/jiip.2007.017

In this paper we improve existing convergence and convergence rate results for the iteratively regularized Gauss-Newton method in two respects: First we show optimal rates of convergence under general source conditions, and second we assume that the linearized equations are solved only approximately in each Newton step. The latter point is important for large scale problems where the linearized equation can often only be solved iteratively, e.g. by the conjugate gradient method.

Key Words: Nonlinear inverse problems,; regularized Newton methods,; source conditions,; convergence rates,; CG-method.

About the article

Published Online: 2007-06-25

Published in Print: 2007-06-19


Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2007.017. Export Citation

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