Posteriori selection strategies of regularization parameters for Lanczos' generalized derivatives

Abstract This paper mainly studies how to select reasonable stepsizes (regularization parameters) in Lanczos’ generalized derivatives. Four posterior selection strategies, in which two strategies need to know the noise level while the other two do not, are proposed with the convergence estimates of regularization solutions (Lanczos’ generalized derivatives). Numerical experiments show that the last three posterior selection strategies, i.e. Posterior Selection Strategies II–IV, are feasible for Lanczos’ generalized derivatives.

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