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Zbl 1198.65101
Mahale, Pallavi; Nair, M.Thamban
A simplified generalized Gauss-Newton method for nonlinear ill-posed problems.
(English)
[J] Math. Comput. 78, No. 265, 171-184 (2009). ISSN 0025-5718; ISSN 1088-6842/e

Summary: Iterative regularization methods for nonlinear ill-posed equations of the form $F(x)= y$, where $F: D(F) \subset X \to Y$ is an operator between Hilbert spaces $X$ and $Y$, usually involve calculation of the Fréchet derivatives of $F$ at each iterate and at the unknown solution $x^\dagger$. In this paper, we suggest a modified form of the generalized Gauss-Newton method which requires the Fréchet derivative of $F$ only at an initial approximation $x_0$ of the solution $x^\dagger$. The error analysis for this method is done under a general source condition which also involves the Fréchet derivative only at $x_0$. The conditions under which the results of this paper hold are weaker than those considered by {\it B. Kaltenbacher} [Numer. Math. 79, No. 4, 501--528 (1998; Zbl 0908.65042)] for an analogous situation for a special case of the source condition.
MSC 2000:
*65J20 Improperly posed problems (numerical methods in abstract spaces)
35R30 Inverse problems for PDE

Citations: Zbl 0908.65042

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