Iteratively regularized Gauss-Newton type methods for approximating quasi-solutions of irregular nonlinear operator equations in Hilbert space with an application to COVID-19 epidemic dynamics.

ABSTRACT

We investigate a class of iteratively regularized methods for finding a quasi-solution of a noisy nonlinear irregular operator equation in Hilbert space. The iteration uses an a priori stopping rule involving the error level in input data. In assumptions that the Frechet derivative of the problem operator at the desired quasi-solution has a closed range, and that the quasi-solution fulfills the standard source condition, we establish for the obtained approximation an accuracy estimate linear with respect to the error level. The proposed iterative process is applied to the parameter identification problem for a SEIR-like model of the COVID-19 pandemic.