Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scales

Lavrentiev's regularization method in Hilbert spaces revisited

“…Note that we will work under assumptions (i), for simplicity of exposition. A comprehensive study of Lavrentiev's regularization method for nonlinear equations in Hilbert spaces with monotone operators, even in a more general setting, can be found in the book [2], for modifications of the method see also [8,9,14,25]. Nevertheless, for completeness of exposition and since some of the estimates will be needed later on, in Section 2 we provide a short summary of the arguments leading to convergence of x δ α from (4) to x † (see also [1,6]).…”