Abstract
We study the choice of the regularisation parameter for linear ill-posed problems in the presence of data noise and operator perturbations, for which a bound on the operator error is known but the data noise level is unknown. We introduce a new family of semi-heuristic parameter choice rules that can be used in the stated scenario. We prove convergence of the new rules and provide numerical experiments that indicate an improvement compared to standard heuristic rules.
Funding source: Austrian Science Fund
Award Identifier / Grant number: P 30157-N31
Funding statement: This work was supported by the Austrian Science Fund (FWF) project P 30157-N31. The research of U. Hämarik and U. Kangro was supported by institutional research funding IUT20-57 of the Estonian Ministry of Education and Research.
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Articles in the same Issue
- Frontmatter
- Inverse space-dependent source problem for a time-fractional diffusion equation by an adjoint problem approach
- On an inverse spectral problem for one integro-differential operator of fractional order
- Parameter identification for the linear wave equation with Robin boundary condition
- Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations
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- A coupled complex boundary expanding compacts method for inverse source problems
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- Semi-heuristic parameter choice rules for Tikhonov regularisation with operator perturbations
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