Figure 4

The algorithmic solvability of the optimisation problem constituted by estimating the cylinder diameter \(d \equiv d_{\text {real}}\) as expressed by the fraction of correct estimations \(|d_{\text {final}} - d_{\text {real}}| < 0.1\, \upmu \hbox {m}\) of all samples considered by the IRGN algorithm, with the initial values \(d_0\) randomly drawn from a range of \([d_{\text {real}} - 50\, \upmu \hbox {m},d_{\text {real}} - 50\, \upmu \hbox {m}]\) (each data point is the average of 200 random initial values). As local minima vanish under increase of \(\kappa \), the algorithm becomes more and more likely to terminate at the correct diameter. A rescaling with respect to the actual diameter \(d_{\text {real}}\) of the ordinate axis brings the different curves for into reasonable agreement. The inset shows the different cases without rescaling. The dashed lines are to guide the eyes only.