  The L-curve method is a well-known heuristic method for choosing the
regularization parameter for ill-posed problems by selecting it according to
the maximal curvature of the L-curve. In this article, we propose a simplified
version that replaces the curvature essentially by the derivative of the
parameterization on the $y$-axis. This method shows a similar behaviour to the
original L-curve method, but unlike the latter, it may serve as an error
estimator under typical conditions. Thus, we can accordingly prove convergence
for the simplified L-curve method.
