A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems
نویسندگان
چکیده
منابع مشابه
A Regularizing Levenberg - Marquardt Scheme , with Applications to Inverse Groundwaterfiltration
The rst part of this paper studies a Levenberg-Marquardt scheme for nonlinear inverse problems where the corresponding Lagrange (or regularization) parameter is chosen from an inexact Newton strategy. While the convergence analysis of standard implementations based on trust region strategies always requires the invertibility of the Fr echet derivative of the nonlinear operator at the exact solu...
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By making use of duality mappings and the Bregman distance, we propose a regularizing Levenberg-Marquardt scheme to solve nonlinear inverse problems in Banach spaces, which is an extension of the one proposed in [6] in Hilbert space setting. The method consists of two components: an outer Newton iteration and an inner scheme. The inner scheme involves a family of convex minimization problems in...
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In this note we study the convergence of the Levenberg-Marquardt regularization scheme for nonlinear ill-posed problems. We consider the case that the initial error satisfies a source condition. Our main result shows that if the regularization parameter does not grow too fast (not faster than a geometric sequence), then the scheme converges with optimal convergence rates. Our analysis is based ...
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The aim of this paper is to construct Levenberg-Marquardt level set methods for inverse obstacle problems, and to discuss their numerical realization. Based on a recently developed framework for the construction of level set methods, we can define LevenbergMarquardt level set methods in a general way by varying the function space used for the normal velocity. In the typical case of a PDE-constr...
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We consider a regularized Levenberg–Marquardt method for solving nonlinear ill-posed inverse problems. We use the discrepancy principle to terminate the iteration. Under certain conditions, we prove the convergence of the method and obtain the order optimal convergence rates when the exact solution satisfies suitable source-wise representations. Mathematics Subject Classification (2000) 65J15 ·...
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ژورنال
عنوان ژورنال: Inverse Problems
سال: 1997
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/13/1/007