Abstract
This paper deals with the numerical solution of ill-posed linear equations. Recently, the author suggested the discrepancy principle as a stopping rule for a certain class of two-step iterative regularization methods developed by Brakhage, the so-called $\nu $-methods. The drawback of that approach is the need for a good estimate of the noise level in the data.Here a new stopping rule for the $\nu $-methods is developed: the update criterion. It is based on a recursive evaluation of the entire iterative process, making use of specific asymptotics of the associated orthogonal polynomials on their interval of orthogonality.The theoretical properties of the update criterion are analyzed and compared with the results of numerical experiments.
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