Abstract
In this paper we investigate Morozov's Discrepancy Principle for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems. Convergence rates and a saturation property of the regularized solutions, where the regularization parameter is chosen by the discrepancy principle, are investigated. Numerical results are presented to verify the theoretical results.
Zusammenfassung
In dieser Arbeit wird das Morozovsche Diskrepanz Prinzip betrachtet, welches bei der Tikhonov Regularisierung zur Lösung eines inkorrekt gestellten Problems zur Wahl des Regularisierungsparameters herangezogen wird. Untersucht werden Konvergenz, Konvergenzraten der regularisierten Lösungen, wenn der Regularisierungsparameter nach dem Morozovschen Diskrepanz Prinzip gewählt wird, und die Saturationseigenschaft dieses Diskrepanz Prinzips. Es werden einige numerische Beispiele zur Untermauerung der theoretischen Resultate präsentiert.
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Scherzer, O. The use of Morozov's discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems. Computing 51, 45–60 (1993). https://doi.org/10.1007/BF02243828
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DOI: https://doi.org/10.1007/BF02243828