Abstract
We consider a new algorithm to solving a linear ill-posed problem with operators of finite smoothness. The algorithm uses a semiiterative method for the regularization of the original problem in combination with an adaptive strategy of discretization. For the operators, the algorithm achieves the optimal order of accuracy. Moreover, it is more economical in the sense of the amount of used discrete information as compared with standard methods.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 7, No. 4, pp. 553–569, October–November, 2010.
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Solodky, S.G., Volynets, E.A. Adaptive scheme of discretization for one semiiterative method in solving ill-posed problems. J Math Sci 175, 477–489 (2011). https://doi.org/10.1007/s10958-011-0357-z
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DOI: https://doi.org/10.1007/s10958-011-0357-z