Extrapolation of Tikhonov regularization method

U. Hämarik, R. Palm, T. Raus
2010 Mathematical Modelling and Analysis  
We consider regularization of linear ill-posed problem Au = f with noisy 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(δ 2/3 ) versus accuracy O(δ 2n/(2n+1) ) of corresponding extrapolated approximation. We propose several rules for choice of the
more » ... f the regularization parameter, some of these are also good in case of moderate over-and underestimation of the noise level. Numerical examples are given.
doi:10.3846/1392-6292.2010.15.55-68 fatcat:uxubgddrdrdvhgt2tqwxds3c6u