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Using the L--curve for determining optimal regularization parameters (1994)

Engl, Heinz W. ; Grever, Wilhelm

Springer

Numerische Mathematik 69 (1994), S. 25-31

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Details

ISSN: 0945-3245

Schlagwort(e): Mathematics Subject Classification (1991):65J20

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Summary. The ``L--curve'' is a plot (in ordinary or doubly--logarithmic scale) of the norm of (Tikhonov--) regularized solutions of an ill--posed problem versus the norm of the residuals. We show that the popular criterion of choosing the parameter corresponding to the point with maximal curvature of the L--curve does not yield a convergent regularization strategy to solve the ill--posed problem. Nevertheless, the L--curve can be used to compute the regularization parameters produced by Morozov's discrepancy principle and by an order--optimal variant of the discrepancy principle proposed by Engl and Gfrerer in an alternate way.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/s002110050078

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