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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 1, 1999, pp. 37–46
DOI: 10.4171/ZAA/868

Published online: 1999-03-31

On Morozov’s Method for Tikhonov Regularization as an Optimal Order Yielding Algorithm

M. Thamban Nair[1]

(1) Indian Institute of Technics, Madras, Chennai, India

It is shown that Tikhonov regularization for an ill-posed operator equation $Kx = y$ using a possibly unbounded regularizing operator $L$ 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 $K$ and $L$ 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.

Keywords: Tikhonov regularization, ill-posed equations, order-optimal algorithms, interpolation inequalities, Hilbert scales

Nair M. Thamban: On Morozov’s Method for Tikhonov Regularization as an Optimal Order Yielding Algorithm. Z. Anal. Anwend. 18 (1999), 37-46. doi: 10.4171/ZAA/868