Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve
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چکیده
منابع مشابه
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...
متن کاملThe 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 "...
متن کاملRegularization 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...
متن کاملOn the Adaptive Selection of the Parameter in Regularization of Ill-Posed Problems
We study a possibility to use the structure of the regularization error for a posteriori choice of the regulatization parameter. As a result, a rather general form of a selection criterion is proposed, and its relation to the heuristical quasi-optimality principle of Tikhonov and Glasko (1964), and to an adaptation scheme propsed in a statistical context by Lepskii (1990), is discussed. The adv...
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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