Regularization of ill-posed problems in Hilbert space by means of the implicit iteration process

Abstract

The article substantiates the convergence of the method with a posteriori choice of the number of iterations in the original norm of Hilbert space in case of a self-adjoint operator on the assumption of existing errors in the equation right-hand member. There has been secured error estimate of the method and the estimate of a posteriori stopping moment. The results obtained can be used in theoretic research while solving linear operator equations as well as in solving applied incorrect problems which occur in dynamics and kinetics, mathematical economics, geophysics, spectroscopy, systems of full automatic procession and interpretation of experiments, plasma diagnostics, seismology, medicine.