JournalszaaVol. 18, No. 1pp. 37–46

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

  • M. Thamban Nair

    Indian Institute of Technics, Madras, Chennai, India
On Morozov’s Method for Tikhonov Regularization as an Optimal Order Yielding Algorithm cover
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Abstract

It is shown that Tikhonov regularization for an ill-posed operator equation Kx=yKx = y using a possibly unbounded regularizing operator LL 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 KK and LL 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. 37–46

DOI 10.4171/ZAA/868