Improved regularizing iterative methods for ill-posed nonlinear systems
For researchers solving nonlinear ill-posed inverse problems, this work provides more robust iterative methods that converge without proximity assumptions.
The paper develops improved iterative regularization methods (Levenberg-Marquardt, trust-region, adaptive quadratic) for solving nonlinear ill-posed systems, demonstrating theoretical regularizing properties and enhanced convergence without requiring the solution to be near the initial guess.
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.