Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kind

Abstract

In this paper, we give necessary and sufficient conditions for weak and strong convergence of general regularization methods for the solution of linear ill-posed problems in Hilbert space. As special cases we obtain convergence criteria for Tychonoff regularization, for a regularization method based on Showalter's integral formula, and for regularization by truncated iteration