Implicit iteration method of solving linear equations with approximating right-hand member and approximately specified operator

Abstract

The article deals with the study of the implicit method of solving linear equations with nonnegative self-adjoint and nonself-adjoint limited operator in Hilbert space. It aims at proving the method convergence in case of a priori choice of the number of iterations in the basic norm of Hilbert space on the assumption of existing errors not only in the equation right-hand member but in the operator as well. Error estimation and a priori stop moment are obtained.