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Improved regularizing iterative methods for ill-posed nonlinear systems

Stefania Bellavia(stefania.bellavia***at***unifi.it)
Benedetta Morini(benedetta.morini***at***unifi.it)

Abstract: In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and noisy data, our focus is on the potential to approach a solution of the unperturbed systems without assumptions on its vicinity to the initial guess. Regularizing properties of the methods proposed are shown theoretically and validated numerically along with enhanced convergence.

Keywords: Ill-posed nonlinear systems of equations, regularization, nonlinear stepsize control,local and global convergence properties.

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation:

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Entry Submitted: 10/10/2014
Entry Accepted: 10/10/2014
Entry Last Modified: 10/10/2014

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