Converse results, saturation and quasi-optimality for Lavrentiev regularization of accretive problems
Provides theoretical foundations for regularization theory, but is incremental as it extends known results to a broader operator class.
The paper establishes converse and saturation results for Lavrentiev regularization of linear ill-posed problems with accretive operators, and proves quasi-optimality of a posteriori parameter choices. Results are extended to Banach spaces.
This paper deals with Lavrentiev regularization for solving linear ill-posed problems, mostly with respect to accretive operators on Hilbert spaces. We present converse and saturation results which are an important part in regularization theory. As a byproduct we obtain a new result on the quasi-optimality of a posteriori parameter choices. Results in this paper are formulated in Banach spaces whenever possible.