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L-curve

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Visualization method

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L-curve is avisualization method used in the field ofregularization innumerical analysis andmathematical optimization.^[1] It represents alogarithmic 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.^[2]

This method can be applied on methods ofregularization of least-square problems, such asTikhonov regularization and the Truncated SVD,^[2] and iterative methods of solvingill-posed inverse problems, such as theLandweber algorithm,Modified Richardson iteration andConjugate gradient method.

References

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^"L-Curve and Curvature Bounds for Tikhonov Regulairzation"(PDF).math.kent.edu. RetrievedJune 15, 2025.
^^a ^bHansen, P. C. (2001). "The L-curve and its use in the numerical treatment of inverse problems". In Johnston, P. R. (ed.).Computational Inverse Problems in Electrocardiography(PDF). WIT Press. pp. 119–142.ISBN 978-1-85312-614-7.

Hanke, Martin. "Limitations of the L-curve method in ill-posed problems." BIT Numerical Mathematics 36.2 (1996): 287-301.
Engl, Heinz W., and Wilhelm Grever. "Using the L--curve for determining optimal regularization parameters." Numerische Mathematik 69.1 (1994): 25-31.

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