What do we Learn from the Discrepancy Principle?

Abstract

The author analyzes the discrepancy principle when smoothness is given in terms of general source conditions. As it turns out, this framework is particularly well suited to reveal the mechanism under which this principle works. For general source conditions there is no explicit way to compute rates of convergence. Instead arguments must be based on geometric properties. Still this approach allows to generalize previous results. The analysis is accomplished with a result showing why this discrepancy principle inherently has the early saturation for a large class of regularization methods of bounded qualification.