Abstract
Nonstationary iterated Tikhonov is an iterative regularization method that requires a strategy for defining the Tikhonov regularization parameter at each iteration and an early termination of the iterative process. A classical choice for the regularization parameters is a decreasing geometric sequence which leads to a linear convergence rate. The early iterations compute quickly a good approximation of the true solution, but the main drawback of this choice is a rapid growth of the error for later iterations. This implies that a stopping criteria, e.g. the discrepancy principle, could fail in computing a good approximation. In this paper we show by a filter factor analysis that a nondecreasing sequence of regularization parameters can provide a rapid and stable convergence. Hence, a reliable stopping criteria is no longer necessary. A geometric nondecreasing sequence of the Tikhonov regularization parameters into a fixed interval is proposed and numerically validated for deblurring problems.
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Donatelli, M. On nondecreasing sequences of regularization parameters for nonstationary iterated Tikhonov. Numer Algor 60, 651–668 (2012). https://doi.org/10.1007/s11075-012-9593-7
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DOI: https://doi.org/10.1007/s11075-012-9593-7