NUMERICAL RESULTS FOR THE PROBLEM OF FINDING A SOLUTION OF A SYSTEM OF ILL-POSED EQUATIONS

Abstract

Many issue s in reality result the problem of finding an unknown quantity x ∈ H from the original data set (f1, . . . , fN) ∈ HN, N ≥ 1, where H is a real Hilbert space. The data set (f1, . . . , fN) which is often not exactly known, is just given approximately by fiδ ∈ H. This problem is modeled by a system of operator equations. Therefore, we need to research and propose a stable solution for the above problem class. The purpose of this paper is to present an iterative regularization method in a real Hilbert space for the problem of finding a solution to a system of nonlinear ill-posed equations. We prove the strong convergence of this method; give an application of the optimal problem and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.