Abstract
In this paper we consider the method of Tikhonov regularization for finding solutions q* of ill-posed linear and nonlinear operator equations A(q) = z, which consists in minimizing the functional Here z ρ are the available perturbed data and is the norm in a Hilbert scale Q s. Assuming for some a ≥0 and γ≥0 we prove that the choice of the regularization parameter α by Morozov's discrepancy principle leads to optimal convergence rates if . Furthermore we discuss convergence rate results for the case and apply our results to a special integral equation of the first kind.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
