А PRIORI CHOICE OF THE REGULARIZATION PARAMETER IN AN ITERATIVE PROCEDURE OF AN EXPLICIT TYPE SOLUTION OF LINEAR ILL-POSED EQUATIONS

Abstract

The explicit iteration procedure with variable-alternating step for solution of ill-posed operator equations of the first kind is proposed in Hilbert space. Convergence of a method is proved in case of a priori choice of the regularization parameter in usual norm of Hilbert space, supposing that not only the right part of the equation but the operator as well have errors. Тhе estimations of an error and a priori stopping moment are received. The results given in the article can be used in theoretical research in solving linear operator equations, as well as in solving applied ill-posed problems.