Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 1, pp. 37-46 (1999)
On Morozov's Method for Tikhonov Regularization as an Optimal Order Yielding Algorithm
M. T. NairM. Thamban Nair: Indian Inst. Techn. Madras, Dept. Math., Chennai 600 036, India
Abstract: 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
Classification (MSC2000): 65R10, 65J10, 65J20, 65R20, 45B05, 45L10, 47A50
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Electronic fulltext finalized on: 25 Apr 2000. This page was last modified: 9 Nov 2001.