On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation

In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a solution of the unperturbed system. This regularizing property is shown theoretically and validated numerically.Comment: arXiv admin note: text overlap with arXiv:1410.278

Irregular nonlinear operator equations: Tikhonov's regularization and iterative approximation

A problem of iterative approximation is investigated for a nonlinear operator equation regularized by the Tikhonov method. The Levenberg-Marquardt method, its modified analogue, and the steepest descent method are used. For the first and second methods the regularizing properties of iterations are established and the error of approximate solution is given. For the third method it was proved that iterations are stabilized in a neighborhood of the required solution and satisfy the strong Fejйr property. © 2013 by Walter de Gruyter Berlin Boston 2013