We consider regularization of linear ill-posed problems Au = ƒ in Hilbert spaces. Approximations ur to the solution u* can be constructed by the Tikhonov method or by the Lavrentiev method, by iterative or by other methods. We assume that instead of ƒ ∈ R(A) noisy data 
are available with the approximately given noise level δ: in process δ → 0 it holds || − ƒ||/δ ≤ c with unknown constant c. We propose a new a-posteriori rule for the choice of the regularization parameter r = r(δ) guaranteeing ur(δ) → u* for δ → 0. Note that such convergence is not guaranteed for the parameter choice given by the L-curve rule, by the GCV-rule, by the quasioptimality criterion and also for discrepancy principle ||Aur − || = bδ with b < c. The error estimates are given, which in case || − ƒ|| ≤ δ are quasioptimal and order-optimal.
Copyright 2006, Walter de Gruyter
