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We consider choice of the regularization parameter in Tikhonov method in thecase of the unknown noise level of the data. From known heuristic parameterchoice rules often the best results were obtained in the quasi-optimalitycriterion where the parameter is chosen as the global minimizer of thequasi-optimality function. In some problems this rule fails, the error of theTikhonov approximation is very large. We prove, that one of the localminimizers of the quasi-optimality function is always a good regularizationparameter. We propose an algorithm for finding a proper local minimizer of thequasi-optimality function.

Heuristic parameter choice in Tikhonov method from minimizers of the quasi-optimality function