Estimation of the Regularization Parameter in Linear Discrete Ill-Posed Problems Using the Picard Parameter
نویسندگان
چکیده
منابع مشابه
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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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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In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing parameter choice methods, and evaluate...
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Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of ...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2017
ISSN: 1064-8275,1095-7197
DOI: 10.1137/17m1123195