Extrapolation of Tikhonov Regularization Method.

We consider regularization of linear ill-posed problem Au = f with noisy data fδ, ∥fδ - f∥ ≤ δ. The approximate solution is computed as the extrapolated Tikhonov approximation, which is a linear combination of n ≥ 2 Tikhonov approximations with different parameters. If the solution u∗ belongs to R((A* A)n), then the maximal guaranteed accuracy of Tikhonov approximation is O(δ2/3) versus accuracy O(δ2n/(2n+1)) of corresponding extrapolated approximation. We propose several rules for choice of the regularization parameter, some of these are also good in case of moderate over- and underestimation of the noise level. Numerical examples are given. [ABSTRACT FROM AUTHOR]