Automatic parameter setting for Arnoldi–Tikhonov methods

Silvia Gazzola, Paolo Novati
2014 Journal of Computational and Applied Mathematics  
In the framework of iterative regularization techniques for large-scale linear ill-posed problems, this paper introduces a novel algorithm for the choice of the regularization parameter when performing the Arnoldi-Tikhonov method. Assuming that we can apply the discrepancy principle, this new strategy can work without restrictions on the choice of the regularization matrix. Moreover this method is also employed as a procedure to detect the noise level whenever it is just overestimated.
more » ... experiments arising from the discretization of integral equations and image restoration are presented.
doi:10.1016/j.cam.2013.07.023 fatcat:waaetw2vgbbbhna5tjqo5r6xzq