Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve

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Regularization Parameter Selection in Discrete Ill-Posed Problems - The Use of the U-Curve

To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This pa...

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The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems

Regularization algorithms are often used to produce reasonable solutions to ill-posed problems. The L-curve is a plot-for all valid regularization parameters-of the size of the regularized solution versus the size of the corresponding residual. Two main results are established. First a unifying characterization of various regularization methods is given and it is shown that the measurement of "...

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Regularization parameter determination for discrete ill-posed problems

Straightforward solution of discrete ill-posed linear systems of equations or leastsquares problems with error-contaminated data does not, in general, give meaningful results, because propagated error destroys the computed solution. The problems have to be modified to reduce their sensitivity to the error in the data. The amount of modification is determined by a regularization parameter. It ca...

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ژورنال

عنوان ژورنال: International Journal of Applied Mathematics and Computer Science

سال: 2007

ISSN: 1641-876X

DOI: 10.2478/v10006-007-0014-3