M.A. Krasnosel’skii theorem and iterative methods for solving ill-posed linear problems with a self-adjoint operator

Abstract

The paper deals with iterative methods for solving linear operator equations x=Bx+f and Ax=f with self-adjoint operators in Hilbert space X in the critical case when ρ(B)=1 and 0∈SpA. The results obtained are based on a theorem by M. A. Krasnosel'skii on the convergence of the successive approximations, their modifications and refinements.