Authors: Heinz Engl and Wilhelm Grever
Abstract: The L-curve is a plot (in ordinary or doubly-logarithmic scale) of the norm of (Tikhonov-) regularized solutions of an ill-posed problem versus the norm of the residuals. We show that the popular criterion of choosing the parameter corresponding to the point with maximal curvature of the L-curve does not yield a convergent regularization strategy to solve the ill-posed problem. Nevertheless, the L-curve can be used to compute the regularization parameters produced by Morozov's discrepancy principle and by an order-optimal variant of the discrepancy principle proposed by Engl and Gfrerer in an alternate way.