منابع مشابه
Multi-Parameter Tikhonov Regularization
We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, t...
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We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a...
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In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minim...
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Abstract. A new parameter choice method for Tikhonov regularization of discrete ill-posed problems is presented. Some of the regularized solutions of a discrete ill-posed problem are less sensitive than others to the perturbations in the right-hand side vector. This method chooses one of the insensitive regularized solutions using a certain criterion. Numerical experiments show that the new met...
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An important issue in quantitative nance is model calibration. The calibration problem is the inverse of the pricing problem. Instead of computing prices in a model with given values for its parameters, one wishes to compute the values of the model parameters that are consistent with observed prices. Now, it is well-known by physicists that such inverse problems are typically ill-posed. So, if ...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2011
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2011.v18.n1.a2