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Eurasian Journal of Mathematical and Computer Applications, 2016, Volume 4, Issue 4, Pages 60–73 (Mi ejmca39)  

Methods for solving nonlinear ill-posed problems based on the Tikhonov-Lavrentiev regularization and iterative approximation

V. V. Vasinab

a Ural Federal University, Lenin Avenue, 51, Ekaterinburg 620000, Russia
b Institute of Mathematics and Mechanics UB RAS, S. Kovalevskay Street, 16,Ekaterinburg 620990, Russia

Abstract: A problem of constructing a stable approximate solution for a nonlinear irregular operator equation is investigated. For approximating solutions of the equations regularized by the Tikhonov-Lavrentiev methods, the Levenberg-Marquardt and Newton type processes are used, and the linear convergence rate and the Fej ́er property are proved. An asymptotic stopping rule of iterations is formulated that guarantees the regularizing properties of iterations and error estimate. Analogous questions are briefly discussed for the gradient methods.

Keywords: ill-posed problem, Tikhonov-Lavrentiev regularization, Levenberg-Marquardt and Newton type methods, stopping rule, error estimate

Full text: https:/.../view
MSC: 45Q05, 65J15, 65J20
Received: 11.10.2016
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