Abstract
This paper considers the Tikhonov regularization method with the regularization parameter chosen by the so-called L-curve criterion. An infinite dimensional example is constructed for which the selected regularization parameter vanishes too rapidly as the noise to signal ratio in the data goes to zero. As a consequence the computed reconstructions do not converge to the true solution. Numerical examples are given to show that similar phenomena can be observed under more general assumptions in “discrete ill-posed problems” provided the exact solution of the problem is “smooth”.
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This work was partially supported by NATO grant CRG 930044.
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Hanke, M. Limitations of the L-curve method in ill-posed problems. Bit Numer Math 36, 287–301 (1996). https://doi.org/10.1007/BF01731984
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DOI: https://doi.org/10.1007/BF01731984