Andreas Rieder 1999 Inverse Problems 15 309 doi:10.1088/0266-5611/15/1/028
Andreas Rieder
Show affiliationsInexact 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.
02.30.Lt Sequences, series, and summability
02.60.Lj Ordinary and partial differential equations; boundary value problems
Issue 1 (February 1999)
Received 24 July 1998
Andreas Rieder 1999 Inverse Problems 15 309
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