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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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Online
ISSN
1569-3945
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Volume 17, Issue 9 (Jan 2009)

Issues

Complexity analysis of the iteratively regularized Gauss–Newton method with inner CG-iteration

S. Langer
  • German Aerospace Center, Member of the Helmholtz Association, Institute of Aerodynamics and Flow Technology, Lilienthalplatz 7, 38108 Braunschweig, Germany. Email:
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Published Online: 2010-01-26 | DOI: https://doi.org/10.1515/JIIP.2009.051

Abstract

In this paper we investigate the numerical complexity to solve nonlinear ill-posed problems when the operator equations F(x) = yδ are solved by the iteratively regularized Gauss–Newton method (IRGNM) with inner CG-iteration. Additionally we consider a preconditioned version of the IRGNM and compare the complexity of the standard IRGNM and its preconditioned version. In the case of exponentially ill-posed problems we show the superiority of the preconditioned IRGNM, that is we prove that the preconditioning techniques presented in this paper yield a significant reduction of the total complexity.

Key words.: Nonlinear inverse problems; regularized Newton methods; CG-method; complexity analysis

About the article

Received: 2009-04-07

Published Online: 2010-01-26

Published in Print: 2009-12-01


Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2009.051.

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