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Applicable Analysis
An International Journal
Volume 18, 1984 - Issue 1-2
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Original Articles

Error bounds for tikhonov regularization in hilbert scales

Frank Natterer Institut fur Numerische und instrumentelle Mathematik, Miinster, West Gemany, D-4400
Pages 29-37 | Published online: 02 May 2007
 
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Abstract

For an ill-posed problem Af = g we consider Tikhonov reguiariration: Minimize where is the norm in a Hilbert scale (Hs). Assuming that the norm is equivalent to the norm for some a > O and f ε Hq for some q > O , we show that the accuracy of Tikhonov regularization is asymptotically best possible, provided that ω is chosen optimally and p ≥ (q - a)/2.

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