Abstract
We consider the problem of approximate solution of severely ill-posed problems with perturbed right-hand sides. The approximation properties of a finite-dimensional version of the Tikhonov regularization in the combination with the a posteriori choice of a regularization parameter by means of the balancing principle are analyzed. It is shown that this approach provides an optimal order of accuracy. The efficiency of the theoretical results is checked by comparison with the earlier known methods.
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Translated from Russian by V. V. Kukhtin
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 8, No. 3, pp. 447–457, July–August, 2011.
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Solodky, S.G., Grushevaya, A.V. On the a posteriori choice of a regularization parameter in the solution of severely ill-posed problems. J Math Sci 181, 98–105 (2012). https://doi.org/10.1007/s10958-012-0678-6
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DOI: https://doi.org/10.1007/s10958-012-0678-6