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L-curve

The L-curve is a graphical tool used in the numerical treatment of linear inverse problems. It displays how the size of a regularized solution varies relative to the size of its residual as a function of a regularization parameter. When the points are plotted in logarithmic scale, the curve typically has a characteristic "L" shape. The flat part of the…

Art, Parameter-choice criterion & Definition

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Parameter-choice criterion

Heuristic methodTruncated singular value decompositionIterative methodsConjugate gradient
4 related topics

Definition

Ill-conditionedRank-deficientTikhonov regularization
3 related topics

Interpretation and properties

Least squares problemsConvex function
2 related topics

Corner and curvature

VertexLanczos bidiagonalization
2 related topics

Topics to explore

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Overview

Definition

Interpretation and properties

Corner and curvature

Parameter-choice criterion

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Map overview Semantic statistics

L-curve

Nodes21
Edges20
Triples45
Avg. degree1.9
Density0.095238
Components1

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L-curve

Top relations

related to history · 10
L-curve → Hansen, Hanson's, L-ribbon, Lawson, Miller's, O'Leary, Subsequent, Tikhonov, Tikhonov’s, Trade-off
related to Interpretation and properties · 7
L-curve → For, Hansen, In, The, The L-curve, Tikhonov, When
related to Limitations · 5
L-curve → Although, Hanke, Hansen's, In, L-shape
related to Corner and curvature · 4
L-curve → Hansen, Let, O'Leary, Writing
related to Definition · 4
L-curve → Consider, In Tikhonov, Let, The L-curve
related to Parameter-choice criterion · 4
L-curve → It, The L-curve, This, Tikhonov
has application · 3
L-curve → It, The, The L-curve
is a · 2
L-curve → graphical tool used in the numerical treatment of linear inverse problems, set of points L

Important terminology Word statistics

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Important terminology

regularization solution displaystyle parameter curve lambda residual corner problems curvature mathbf norm criterion large used inverse also regularized tikhonov hansen

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
L-curveis agraphical tool used in the numerical treatment of linear inverse problems0.90text
L-curveis aset of points L0.90text
conjugate gradient on the normal equations by treating the iteration index as a discrete regularization parameterinstance ofIt can also be adapted to iterative methods0.80text
tomographyinstance ofApplicationsThe L-curve is widely employed in inverse problems arising in fields0.80text
geoscienceinstance ofApplicationsThe L-curve is widely employed in inverse problems arising in fields0.80text
deconvolutioninstance ofApplicationsThe L-curve is widely employed in inverse problems arising in fields0.80text
the L-ribboninstance ofand proposed alternatives0.80text
curvature-ribboninstance ofand proposed alternatives0.80text
L-curvehas applicationThe L-curve0.60section
L-curvehas applicationIt0.60section
L-curvehas applicationThe0.60section
L-curverelated to Corner and curvatureHansen0.60section

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