Error bounds for tikhonov regularization in hilbert scales

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.