On the conditions of convergence for one class of methods used for the solution of ill-posed problems

Abstract

We propose a new class of projection methods for the solution of ill-posed problems with inaccurately specified coefficients. For methods from this class, we establish the conditions of convergence to the normal solution of an operator equation of the first kind. We also present additional conditions for these methods guaranteeing the convergence with a given rate to normal solutions from a certain set.