Extrapolation of Tikhonov and Lavrentiev regularization methods

@inproceedings{Hmarik2008ExtrapolationOT,
  title={Extrapolation of Tikhonov and Lavrentiev regularization methods},
  author={Uno H{\"a}marik and Toomas Raus},
  year={2008}
}
We consider solution of linear ill-posed problem Au = f by Tikhonov method and by Lavrentiev method. For increasing the qualification and accuracy of these methods we use extrapolation, taking for the approximate solution linear combination of n ≥ 2 approximations of Tikhonov or Lavrentiev methods with different parameters and with proper coefficients. If the solution u∗ belongs to R((A A)) and instead of f noisy data fδ with ‖fδ − f‖ ≤ δ are available, maximal guaranteed accuracy of Tikhonov… CONTINUE READING

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