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• W2109023033 abstract "We discuss a new a posteriori rule for choosing the regularization parameter in regularization methods for solving linear ill-posed problems Ax = y with minimum-norm solution x. Main emphasis is devoted to the methods of ordinary and iterated Tikhonov regularization. We suppose that instead of y there are given noisy data y satisfying |y-y| with known noise level . The approach of the new rule consists of finding the smallest = ME for which it can be proved that the error |x-x| of the regularized solution xisstrictlymonotonicallyincreasingforincreasing-values, that is, there holds {d}{{dalpha}}|x-x|2>0 for all (ME,). Due to this property we call our rule of choosing the monotone error rule (ME rule). Our ME rule leads to smaller errors than the a posteriori rule of Raus (1985 Acta Comment. Univ. Tartuensis 715 12-20 (in Russian)) and Gfrerer (1987 Math. Comput. 49 507-22). Furthermore, we discuss discretization issues and illustrate some of our theoretical results by numerical experiments." @default.
• W2109023033 created "2016-06-24" @default.
• W2109023033 creator A5010598640 @default.
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• W2109023033 date "1999-12-01" @default.
• W2109023033 modified "2023-09-26" @default.
• W2109023033 title "The use of monotonicity for choosing the regularization parameter in ill-posed problems" @default.
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• W2109023033 doi "https://doi.org/10.1088/0266-5611/15/6/307" @default.
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