Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]