Generalized qualification and qualification levels for spectral regularization methods (Q1035881)

The authors state that the concept of qualification for spectral regularization methods (SRM) for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. They extend the definition of qualification and introduce three different levels of qualification namely, weak, strong and optimal. It is contended that weak qualification extends the definition introduced by \textit{P. Mathe} and \textit{S. V. Pereverzev} [Inverse Probl. 19, No. 3, 789--803 (2003; Zbl 1026.65040)]. Sufficient conditions for a SRM to have weak qualification are given. Moreover, necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are obtained. Examples of all three levels of qualification are given and relationships between them as well as with the classified concept of qualification and the qualification introduced by Mathe and Pereverzev in the above mentioned reference are examined.