Regularization parameter determination for discrete ill-posed problems
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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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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In many science and engineering applications, the discretization of linear illposed problems gives rise to large ill-conditioned linear systems with right-hand side degraded by noise. The solution of such linear systems requires the solution of a minimization problem with one quadratic constraint depending on an estimate of the variance of the noise. This strategy is known as regularization. In...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2015
ISSN: 0377-0427
DOI: 10.1016/j.cam.2014.06.004