English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition.

MPS-Authors
/persons/resource/persons129903

Werner,  F.
Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society;

External Ressource
No external resources are shared
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Werner, F. (2015). On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition. Journal of Inverse and III-posed Problems, 23(1), 75-84. doi:10.1515/jiip-2013-0074.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0018-EC16-7
Abstract
We investigate a generalization of the well-known iteratively regularized Gauss–Newton method where the Newton equations are regularized variationally using general data delity and penalty terms. To obtain convergence rates, we use a general error assumption which has recently been shown to be useful for impulsive and Poisson noise. We restrict the nonlinearity of the forward operator only by a Lipschitztype condition and compare our results to other convergence rates results proven in the literature. Finally we explicitly state our convergence rates for the aforementioned case of Poisson noise to shed some light on the structure of the posed error assumption.