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.