Convergence rates for Tikhonov regularization from different kinds of smoothness conditions

摘要: The article is concerned with ill-posed operator equations Ax = y where A:X →Y an injective bounded linear non-closed range and X Y are Hilbert spaces. solution x=x † assumed to be in the of some selfadjoint strictly positive G:X →X. Under several assumptions on G, such as or more generally , inequalities form inclusions convergence rates for regularization error Tikhonov established. We also show that part our automatically imply so-called source conditions. contains a series new results but intends uncover cross-connections between different kinds smoothness conditions have been discussed literature regularization.