It is shown that Tikhonov regularization for an ill-posed operator equation using a possibly unbounded regularizing operator yields an order-optimal algorithm with respect to certain stability set when the regularization parameter is chosen according to Morozov’s discrepancy principle. A more realistic error estimate is derived when the operators and are related to a Hilbert scale in a suitable manner. The result includes known error estimates for ordininary Tikhonov regularization and also estimates available under the Hilbert scales approach.
Cite this article
M. Thamban Nair, On Morozov’s Method for Tikhonov Regularization as an Optimal Order Yielding Algorithm. Z. Anal. Anwend. 18 (1999), no. 1, pp. 37–46DOI 10.4171/ZAA/868