On convergence rates for asymptotic discrepancy principle
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Anatoly Bakushinsky
Abstract
A series of recent numerical experiments for parameter estimation inverse problems in epidemiology [7, 6] have indicated that applicability of the discrepancy principle (DP) does not depend on the structure of a particular regularizing operator. This observation confirmed the original theoretical analysis by Bakushinsky [1, 2] on the construction of fairly general stabilizing algorithms in Banach and Hilbert spaces. In [7, 6], a unified approach to the implementation of the DP for linear ill-posed problems, the Abstract Discrepancy Principle, has been proposed and justified. The current paper investigates the convergence rates of the ADP. Special cases of sectorial and self-adjoint operators are studied.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1112897
Funding statement: This work is supported by NSF under grant (DMS-1112897).
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
