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A numerical method for solving nonlinear ill-posed problems

By Ruben G. Airapetyan, Alexander G. Ramm and Alexandra B. Smirnova


The goal of this paper is to develop a general approach to solution of ill-posed nonlinear problems in a Hilbert space based on continuous processes with a regularization procedure. To avoid the illposed inversion of the Fréchet derivative operator a regularizing oneparametric family of operators is introduced. Under certain assumptions on the regularizing family a general convergence theorem is proved. The proof is based on a lemma describing asymptotic behavior of solutions of a new nonlinear integral inequality. Then the applicability of the theorem to the continuous analogs of the Newton, Gauss-Newton and simple iteration methods is demonstrated

Year: 2000
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