On Minimization Strategies for Choice of the Regularization Parameter in Ill-Posed Problems

We consider solving of linear ill-posed problems using the Tikhonov method (in self-adjoint case the Lavrentiev method), its iterated variant, Landweber method and conjugate gradient type methods. Several rules for a posteriori choice of the regularization parameter are proposed. In case of known noise level of data we propose to compute in Tikhonov method certain 2 parameters and take for regularization parameter minimal of them. In case of unknown noise level we consider family of rules where a certain function is minimized. The quasioptimality criterion and Hanke-Raus rule are included, error estimates are given. Extensive numerical experiments show an advantage of proposed rules over known rules.

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