Thu, 23 July, 2009, 17:15-18:15, Foyer
We consider linear ill-posed problem with noisy data in Hilbert space. The approximations to the solution are found by the Tikhonov method or by the Lavrentiev method or by iterated or extrapolated variants of these methods. For choice of the regularization parameter we propose the following minimization strategy. In case of known noise level we take for the parameter minimum of certain expressions of parameters from the monotone error rule and from the new rule R2. In case of roughly given or unknown noise level we propose to take for the regularization parameter the minimizer of certain functional, which is an analog of the functional from the quasioptimality criterion. The starting point of the minimization interval is in case of roughly given noise level determined by another parameter choice rule R1 and will be determined in case of unknown noise level from increase condition of the functional to be minimized. Results of extensive numerical experiments are given.
Presentation slides (pdf, 151 KB)
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