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• W3113450000 abstract "A main drawback of classical Tikhonov regularization is that often the parameters required to apply theoretical results, e.g., the smoothness of the sought-after solution and the noise level, are unknown in practice. In this paper we investigate in new detail the residuals in Tikhonov regularization viewed as functions of the regularization parameter. We show that the residual carries, with some restrictions, the information on both the unknown solution and the noise level. By calculating approximate solutions for a large range of regularization parameters, we can extract both parameters from the residual given only one set of noisy data and the forward operator. The smoothness in the residual allows to revisit parameter choice rules and relate a-priori, a-posteriori, and heuristic rules in a novel way that blurs the lines between the classical division of the parameter choice rules. All results are accompanied by numerical experiments." @default.
• W3113450000 created "2021-01-05" @default.
• W3113450000 creator A5079317425 @default.
• W3113450000 creator A5083407680 @default.
• W3113450000 date "2020-12-29" @default.
• W3113450000 modified "2023-09-27" @default.
• W3113450000 title "Estimating solution smoothness and data noise with Tikhonov regularization" @default.
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