Optimality for ill-posed problems under general source conditions

摘要: In this paper we consider linear ill-posed problems where instead of y noisy data yδ are available with and is a operator between Hilbert spaces X Y. Assuming the general source condition appropriate functions φ study following questions:(i) which (best possible) accuracy can be obtained for identifying x from under assumptions (ii) there special regularization methods guarantee best possible accuracy, i.e., optimal on set Mδ,E? Concerning question (i) prove that certain conditions holds inf sup ‘inf’ taken over all 'sup' .and optimality class specify our results to Tikhonov type spectral methods. Heat equation backward in time characterized by different φ(λ) serve as model examples.