Abstract
We consider the nonlinear inverse problem of identifying a parameter from knowledge of the physical state in an elliptic partial differential equation. For a derivative free Landweber method, convergence rates are proven under a weak source condition not involving the standard Fréchet derivative of the nonlinear parameter-to-output map. This source condition is discussed both for the estimation of state- and space-dependent parameters in higher dimensions. Finally, numerical results are presented.
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This work was supported by the Austrian National Science Foundation FWF under grant SFB F013 project F1308.
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Kügler, P. Convergence rate analysis of a derivative free landweber iteration for parameter identification in certain elliptic PDEs. Numer. Math. 101, 165–184 (2005). https://doi.org/10.1007/s00211-005-0609-2
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DOI: https://doi.org/10.1007/s00211-005-0609-2