Abstract
In this paper we consider the regularization method applied to an ill-posed problem including Fredholm integral equation of the first kind. The method reduces to the determination of the optimal regularization parameter. To estimate the optimal parameter for a certain class of problems, we first define a subset of the semi-infinite interval [0, ∞) called the optimal region and prove that the optimal parameter lies in the region. Next we introduce a function to estimate the optimal region and show that the function is a good estimator for the class of problems.
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Kitagawa, T. A deterministic approach to optimal regularization —The finite dimensional case—. Japan J. Appl. Math. 4, 371–391 (1987). https://doi.org/10.1007/BF03167812
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DOI: https://doi.org/10.1007/BF03167812