Regularized collocation method for Fredholm integral equations of the first kind
Journal of Complexity
Elastic-net regularization in learning theory
Journal of Complexity
Approximate inverse method for stable analytic continuation in a strip domain
Journal of Computational and Applied Mathematics
A New Regularization Method for the Time Fractional Inverse Advection-Dispersion Problem
SIAM Journal on Numerical Analysis
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We study the possibility of using the structure of the regularization error for a posteriori choice of the regularization parameter. As a result, a rather general form of a selection criterion is proposed, and its relation to the heuristical quasi-optimality principle of Tikhonov and Glasko [Z. Vychisl. Mat. Mat. Fiz., 4 (1964), pp. 564-571] and to an adaptation scheme proposed in a statistical context by Lepskii [Theory Probab. Appl., 36 (1990), pp. 454-466] is discussed. The advantages of the proposed criterion are illustrated by using such examples as self-regularization of the trapezoidal rule for noisy Abel-type integral equations, Lavrentiev regularization for nonlinear ill-posed problems, and an inverse problem of the two-dimensional profile reconstruction.