On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition
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Frank Werner
Abstract
We investigate a generalization of the well-known iteratively regularized Gauss–Newton method where the Newton equations are regularized variationally using general data fidelity 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 Lipschitz-type 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.
Funding source: DFG
Award Identifier / Grant number: SFB 755
Funding source: DFG
Award Identifier / Grant number: Research Training Group 1023
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Inverse problems for linear degenerate parabolic equations by “time-like” Carleman estimate
- Spectral problems and scattering on noncompact star-shaped graphs containing finite rays
- Stability estimates for Burgers-type equations backward in time
- A Hölder-logarithmic stability estimate for an inverse problem in two dimensions
- On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition
- Identification of an unknown spatial load distribution in a vibrating cantilevered beam from final overdetermination
Articles in the same Issue
- Frontmatter
- Inverse problems for linear degenerate parabolic equations by “time-like” Carleman estimate
- Spectral problems and scattering on noncompact star-shaped graphs containing finite rays
- Stability estimates for Burgers-type equations backward in time
- A Hölder-logarithmic stability estimate for an inverse problem in two dimensions
- On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition
- Identification of an unknown spatial load distribution in a vibrating cantilevered beam from final overdetermination
