Abstract
The properties of a quasi-optimal choice of the regularization parameter for the extremum of the smoothing Tikhonov functional for a linear equation of the first kind in an infinitely dimensional Hilbert space are studied; this is done within the limits of absolutely exact calculations. The concept of an automatically regularizing parameter is introduced, and a certain subset in the set of all kinds of initial data of the problem is separated in such a way that an algorithm based on the quasi-optimality principle has automatically regularizing properties on this subset.
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