A simplified generalized Gauss-Newton method for nonlinear ill-posed problems

Authors:
Pallavi Mahale and M. Thamban Nair

Journal:
Math. Comp. **78** (2009), 171-184

MSC (2000):
Primary 65J20

DOI:
https://doi.org/10.1090/S0025-5718-08-02149-2

Published electronically:
June 10, 2008

MathSciNet review:
2448702

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Abstract: Iterative regularization methods for nonlinear ill-posed equations of the form , where is an operator between Hilbert spaces and , usually involve calculation of the Fréchet derivatives of at each iterate and at the unknown solution . In this paper, we suggest a modified form of the generalized Gauss-Newton method which requires the Fréchet derivative of only at an initial approximation of the solution . The error analysis for this method is done under a general source condition which also involves the Fréchet derivative only at . The conditions under which the results of this paper hold are weaker than those considered by Kaltenbacher (1998) for an analogous situation for a special case of the source condition.

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Additional Information

**Pallavi Mahale**

Affiliation:
Department of Mathematics, IIT Madras, Chennai 600036, India

Email:
pallavimahale@iitm.ac.in

**M. Thamban Nair**

Affiliation:
Department of Mathematics, IIT Madras, Chennai 600036, India

Email:
mtnair@iitm.ac.in

DOI:
https://doi.org/10.1090/S0025-5718-08-02149-2

Received by editor(s):
July 2, 2007

Received by editor(s) in revised form:
January 13, 2008

Published electronically:
June 10, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.