A new L-curve for ill-posed problems
نویسندگان
چکیده
منابع مشابه
Ill-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
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In many applications, the discretization of continuous ill-posed inverse problems results in discrete ill-posed problems whose solution requires the use of regularization strategies. The L-curve criterium is a popular tool for choosing good regularized solutions, when the data noise norm is not a priori known. In this work, we propose replacing the original ill-posed inverse problem with a nois...
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In this paper, we propose a new method for solving large-scale ill-posed problems. This method is based on the Karush–Kuhn–Tucker conditions, Fisher–Burmeister function and the discrepancy principle. The main difference from the majority of existing methods for solving ill-posed problems is that, we do not need to choose a regularization parameter in advance. Experimental results show that the ...
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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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When discrete ill-posed problems are analyzed and solved by various numerical regularization techniques, a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector. In particular, the graph associated with Tikhonov regularization plays a central role. The main purpose of this paper is to advo...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2008
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.01.025