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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Vydáno v:	Numerische Mathematik Ročník 115; číslo 2; s. 229 - 259
Hlavní autor:	Jin, Qinian
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer-Verlag 01.04.2010 Springer
Témata:	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
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Shrnutí:	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