Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales
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Andreas Neubauer
Abstract
In this paper we derive convergence rates results for Landweber iteration in Hilbert scales. The assumptions that are necessary to prove these results are less restrictive than the ones given in an earlier paper. The relaxed conditions enlarge the range of applicability to a much wider class of nonlinear problems. The theory is applied to nonlinear Hammerstein operators.
References
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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Inversions of the windowed ray transform
- Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs–Divisia indices and forecasting
- Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales
- An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter
- Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems
- Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems
- Accuracy estimates of Gauss–Newton-type iterative regularization methods for nonlinear equations with operators having normally solvable derivative at the solution
- On convergence rates for asymptotic discrepancy principle
- Identification of an unknown coefficient in KdV equation from final time measurement
- Improved asymptotic analysis for dynamical probe method
Artikel in diesem Heft
- Frontmatter
- Inversions of the windowed ray transform
- Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs–Divisia indices and forecasting
- Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales
- An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter
- Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems
- Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems
- Accuracy estimates of Gauss–Newton-type iterative regularization methods for nonlinear equations with operators having normally solvable derivative at the solution
- On convergence rates for asymptotic discrepancy principle
- Identification of an unknown coefficient in KdV equation from final time measurement
- Improved asymptotic analysis for dynamical probe method
