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Convergence Analysis of Levenberg-Marquardt Method for Inverse Problem with H\"{o}lder Stability Estimate

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arxiv 2501.08932 v1 pith:2DG52BLO submitted 2025-01-15 math.FA

Akari Ishida , Sei Nagayasu , Gen Nakamura This is my paper
classification math.FA
keywords convergenceinverseproblemsanalysisestimatelderlevenberg-marquardtmethod
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We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder stability estimate. Furthermore, based on what we found in the mentioned analysis, we develop global reconstruction algorithms for solving inverse problems with finite measurements for exact and noisy data, respectively.

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