L-Curve

L-Curve

A graphical representation of the distribution of income in which the income of high earners vastly outweighs the income of all others. On an L-curve, the x-axis represents population and the y-axis represents income. The more income one earns in a year, the higher one's place on the L-curve. The curve increases gradually until it reaches the very wealthy, at which point it increases exponentially.
References in periodicals archive ?
GREVER, Using the L-Curve for Determining Optimal Regularization Parameters, Numer.
HANKE, Limitations of the L-Curve Method in Ill-posed Problems, BIT, 36 (1996), no.
VOGEL, Non-convergence of the L-curve Regularization Parameter Selection Method, Inverse Problems, 12 (1996), no.
The L-curve is often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side contaminated by errors of unknown norm.
Ill-posed problem, regularization, L-curve, Gauss quadrature.
Hansen and O'Leary [10, 13] propose to choose the value of the parameter [mu] that corresponds to the point at the "vertex" of the "L," where the vertex is defined to be the point on the L-curve with curvature [[kappa].
Similar approaches, coupled with parameter selection techniques such as the discrepancy principle, the generalized cross validation (GCV), and the L-curve were then studied in [2,3,31,32,47,61].
Obviously, the situation is even more pronounced whenever [parallel]e[parallel] is not known, and then other stopping rules such as the GCV or the L-curve need to be used.
16, 40, 66]), in our experiments we use the L-curve criterion based on the adaptive algorithm referred to as "pruning algorithm" [39].
As particular examples, we study in detail the Hanke-Raus rules, the quasi-optimality rules (continuous and discrete) and to a lesser extent the L-curve method.
Furthermore, in this section, we explain the drawback of the L-curve method.
the (modified) L-curve method with parameter [mu] > 0,