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On a class of frozen regularized Gauss-Newton methods for nonlinear inverse problems


Author: Qinian Jin
Journal: Math. Comp. 79 (2010), 2191-2211
MSC (2010): Primary 65J15, 65J20
DOI: https://doi.org/10.1090/S0025-5718-10-02359-8
Published electronically: April 20, 2010
MathSciNet review: 2684361
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Abstract: In this paper we consider a class of regularized Gauss-Newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration. Such methods have the frozen feature that they require only the computation of the Fréchet derivative at the initial approximation. Thus the computational work is considerably reduced. Under certain mild conditions, we give the convergence analysis and derive various estimates, including the order optimality, on these methods.


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Additional Information

Qinian Jin
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061
Email: qjin@math.utexas.edu, qnjin@math.vt.edu

DOI: https://doi.org/10.1090/S0025-5718-10-02359-8
Keywords: Nonlinear inverse problems, frozen regularized Gauss-Newton method, a posteriori stopping rule, convergence, order optimality
Received by editor(s): September 26, 2008
Received by editor(s) in revised form: June 1, 2009
Published electronically: April 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.