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On the regularization of nonlinear ill-posed problems via inexact Newton iterations

Andreas Rieder

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Inexact Newton methods for the stable solution of nonlinear ill-posed problems are considered. The corresponding inner scheme can be chosen to be any linear regularization with a sufficient modulus of convergence. The regularization property of these Newton-type algorithms is verified, that is, the iterates converge to a solution of the nonlinear problem with exact data when the noise level tends to zero. Moreover, convergence rates are given. Finally, implementation issues are discussed and the algorithm is applied to a parameter identification problem for an elliptic PDE. The numerical results reproduce nicely theoretical predictions and show the efficiency of the proposed method.


PACS

02.30.Lt Sequences, series, and summability

02.60.Lj Ordinary and partial differential equations; boundary value problems

02.30.Jr Partial differential equations

MSC

35Rxx Miscellaneous topics involving partial differential equations (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see also 60H15)

Subjects

Mathematical physics

Computational physics

Dates

Issue 1 (February 1999)

Received 24 July 1998



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