Abstract
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.
ACKNOWLEDGMENT
This work was supported by the Estonian Science Foundation Research Grant No. 7489.