On a regularized Levenberg–Marquardt method for solving nonlinear inverse problems

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...

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Bibliographic Details
Published in:Numerische Mathematik Vol. 115; no. 2; pp. 229 - 259
Main Author: Jin, Qinian
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.04.2010
Springer
Subjects:
Acceleration of convergence
Exact sciences and technology
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical and Computational Physics
Numerical linear algebra
Sciences and techniques of general use
Simulation
Theoretical
65J15
47H17
65J20
Convergence acceleration
Numerical linear algebra
Iteration
Nonlinear problems
Optimal convergence
Inverse problem
Exact solution
Regularization method
Numerical analysis
Problem solving
Convergence rate
Optimal approximation
Ill posed problem
ISSN:0029-599X, 0945-3245
Online Access:Get full text
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Description
Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-009-0275-x