# 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 ?
Finally, for the sake of comparison, we also computed the optimal [lambda] value obtained from the standard L-curve method .
The mean optimal lambda obtained with the L-curve was 1e - 10.
For comparison, we also used a standard procedure known as the L-curve approach to identify an optimal Tikhonov regularization from our simulated data.
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" .
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.
Numerical experiments show that the new method is competitive with the popular L-curve method.
A popular method for choosing a proper regularization parameter is the L-curve criterion given by Hansen and O'Leary .
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.
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