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.
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For example, the generalized cross-validation (GCV) method [17], the L-curve method [18], the U-curve method [19], the variational Bayesian framework [9], and the discrepancy principle [20].
In the next experiment, adaptive selection of [lambda] using the proposed method is compared with GCV [17] and L-Curve [18] methods which are applied for automatic selection of regularizing parameter.
Fifth, the L-curve criteria, combined with the IME regularization technique, are applied to select the suitable regularization parameter for dynamic force identification in complex vibration system.
Moreover, by analogy of the L-curve method [17], we calculate the optimal value of the regularization parameter by determining an expression for the inflection point of the curve.
Finally, for the sake of comparison, we also computed the optimal [lambda] value obtained from the standard L-curve method [51].
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].
The still remaining nonuniqueness can be overcome by using appropriate regularization methods, such as Tikhonov regularization and the L-curve technique [3], in which a certain quadratic functional of the velocity, for example, the kinetic energy or the squared curvature, is additionally minimized.
EVM is established on the notion that both estimated and actual performance are constant over time; however, in many knowledge-based companies, performance generally follows a nonlinear L-curve (Figure 2).
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.
Various techniques can be used, such as the discrepancy principle, the L-curve, and generalized cross validation (GCV) [8, 18, 32].
Numerical experiments show that the new method is competitive with the popular L-curve method.
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.