L-curve

{{Short description|Visualization method}}

{{Regression bar}}

L-curve is a visualization method used in the field of regularization in numerical analysis and mathematical optimization.{{Cite web |title=L-Curve and Curvature Bounds for Tikhonov Regulairzation |url=https://www.math.kent.edu/~reichel/publications/tikcrvL.pdf |access-date=June 15, 2025 |website=math.kent.edu |format=PDF}} It represents a logarithmic plot where the norm of a regularized solution is plotted against the norm of the corresponding residual norm. It is useful for picking an appropriate regularization parameter for the given data.{{cite book |last=Hansen |first=P. C. |date=2001 |editor-last=Johnston |editor-first=P. R. |title=Computational Inverse Problems in Electrocardiography |publisher=WIT Press |pages=119–142 |chapter=The L-curve and its use in the numerical treatment of inverse problems |isbn=978-1-85312-614-7 |url=https://www.sintef.no/globalassets/project/evitameeting/2005/lcurve.pdf}}

This method can be applied on methods of regularization of least-square problems, such as Tikhonov regularization and the Truncated SVD, and iterative methods of solving ill-posed inverse problems, such as the Landweber algorithm, Modified Richardson iteration and Conjugate gradient method.