ar X iv : m at h - ph / 9 91 10 41 v 1 2 7 N ov 1 99 9 Continuous methods for solving nonlinear ill - posed problems
نویسنده
چکیده
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 ill-posed inversion of the Fréchet derivative operator a regularizing one-parametric 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. AMS subject classification: Primary: 47H17. Secondary: 65J15, 58C15.
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