ITERATION METHOD OF EXPLICIT TYPE FOR SOLVING INCORRECT EQUATIONS OF FIRST KIND WITH APPROXIMATELY SPECIFIED OPERATOR

Abstract

The article deals with the study of the explicit method of solving incorrect equations of the first kind with nonnegative self-adjoint limited operator in Hilbert space. It aims at proving the method convergence in case of a priori and a posteriori 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, a priori stop moment and estimate for the а posteriori moment stop are obtained.