Iteration method of a non-explicit solution type of the incorrect problems in the Hilbert space
The new iteration method of solution of the first-kind operator equations with a self-conjugated and non-self-conjugated positive bounded operator in the Hilbert space is proposed. Convergence of a method in case of an apriori choice of number of iterations in usual and energy norm of Hilbert space has been investigated; estimation of errors is received. The opportunity of the application of a rule residual stop and the rule of neighboring approximations are proved for the offered method. The case of non-uniqueness of the solution of the equation is investigated. The comparison of the error estimations of the given iteration method and the evident method of simple iteration has been done.