An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method
-
Fábio Margotti
and
Andreas Rieder
Abstract
A version of the nonstationary iterated Tikhonov method was recently introduced to regularize linear inverse problems in Banach spaces [Inverse Problems 28 (2012), Article ID 104011]. In the present work we employ this method as inner iteration of the inexact Newton regularization method REGINN [Inverse Problems 15 (1999), 309–327] which stably solves nonlinear ill-posed problems. Further, we propose and analyze a Kaczmarz version of the new scheme which allows fast solution of problems which can be split into smaller subproblems. As special cases we prove strong convergence of Kaczmarz variants of the Levenberg–Marquardt and the iterated Tikhonov methods in Banach spaces.
Funding source: German Academic Exchange Service (DAAD)
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity
- Ill-conditioning versus ill-posedness for the boundary controllability of the heat equation
- Parameters identification in the mathematical model of immune competition cells
- Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
- Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses
- An inverse problem for the Vlasov–Poisson system
- An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method
- Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
- The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
Articles in the same Issue
- Frontmatter
- The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity
- Ill-conditioning versus ill-posedness for the boundary controllability of the heat equation
- Parameters identification in the mathematical model of immune competition cells
- Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
- Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses
- An inverse problem for the Vlasov–Poisson system
- An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method
- Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
- The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
