M.A. Krasnoselskii theorem and iteration methods of solving ill-posed linear problems with a self-adjoint operator

O. V. Matysik; P. P. Zabreiko

paper

M.A. Krasnoselskii theorem and iteration methods of solving ill-posed linear problems with a self-adjoint operator

arXiv:1412.1222

Abstract

The article deals with iterative methods of solving linear operator equations $x = B x + f$ and $A x = f$ with self-adjoint operators in Hilbert space $X$ in critical case when $ρ (B) = 1$ and $0 \in Sp A$ . The main results are based on the use of M.A. Krasnosel'skiĭ theorem about the convergence of the successive approximations and some its modifications and refinements.

22 pages