The problem of identifying the unknown of the ill-posed inverse problem is studied, where is a linear bounded operator between infinite-dimensional Hilbert spaces and with non-closed range of and, ; , ( denotes an initial approximation for the problem ) with appropriate functions . As regards accuracy which can be obtained for identifying from it is proved that under certain conditions
holds with , where inf is taken over all methods and the sup is taken over all and . In addition, it is proved the optimality of a general class of regularization methods which guarantee this best possible accuracy. In this general class Tikhonov methods and spectral methods are special cases. Different classes of examples are discussed.