Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792

CiteScore 2016: 0.80

SCImago Journal Rank (SJR) 2016: 0.589
Source Normalized Impact per Paper (SNIP) 2016: 1.125

Mathematical Citation Quotient (MCQ) 2015: 0.43

See all formats and pricing
More options …
Volume 18, Issue 4 (Jan 2010)


Discrepancy principle for generalized GN iterations combined with the reverse connection control

Anatoly Bakushinsky / Alexandra Smirnova
  • Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2010-10-20 | DOI: https://doi.org/10.1515/jiip.2010.019


In this paper we investigate the generalized Gauss–Newton method in the following form

x n+1 = ξn θ(F′*(xn )F′(xn ), τn )F′*(xn ){(F(xn ) – ƒδ) – F′(xn )(xn ξn )}, x 0, ξn ∈ 𝒟 ⊂ H 1.

The modified source condition

which depends on the current iteration point xn , is used. We call this inclusion the undetermined reverse connection. The new source condition leads to a much larger set of admissible control elements ξn as compared to the previously studied versions, where ξn = ξ. The process is combined with a novel a posteriori stopping rule, where is the number of the first transition of ‖F(xn ) – ƒδ‖ through the given level δω , 0, < ω < 1, i.e.,

The convergence analysis of the proposed algorithm is given.

Keywords.: Stopping rule; discrepancy principle; ill-posed problem; iterative regularization; Fréchet derivative; Gauss–Newton's method

About the article

Received: 2010-04-01

Published Online: 2010-10-20

Published in Print: 2010-10-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2010.019.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

A. Smirnova, A. Bakushinsky, and L. DeCamp
Applicable Analysis, 2015, Volume 94, Number 4, Page 672
Alexandra Smirnova
Inverse Problems, 2012, Volume 28, Number 8, Page 085005

Comments (0)

Please log in or register to comment.
Log in