Barbara Kaltenbacher et al 2009 Inverse Problems 25 065003 doi:10.1088/0266-5611/25/6/065003
Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems
Barbara Kaltenbacher1, Frank Schöpfer2 and Thomas Schuster2,3
Show affiliationsIn this paper, we study convergence of two different iterative regularization methods for nonlinear ill-posed problems in Banach spaces. One of them is a Landweber type iteration, the other one the iteratively regularized Gauss–Newton method with an a posteriori chosen regularization parameter in each step. We show that a discrepancy principle as a stopping rule renders these iteration schemes regularization methods, i.e., we prove their convergence as the noise level tends to zero. The theoretical findings are illustrated by two parameter identification problems for elliptic PDEs.
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Issue 6 (June 2009)
Received 21 November 2008, in final form 3 March 2009
Published 9 April 2009
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Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems
Barbara Kaltenbacher et al 2009 Inverse Problems 25 065003
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