DISCRETIZATION ERROR ANALYSIS FOR TIKHONOV REGULARIZATION
نویسندگان
چکیده
منابع مشابه
Discretization Error Analysis for Tikhonov Regularization
Received (Day Month Year) Revised (Day Month Year) We study the discretization of inverse problems defined by a Carleman operator. In particular we develop a discretization strategy for this class of inverse problems and we give a convergence analysis. Learning from examples as well as the discretization of integral equations can be analysed in our setting.
متن کاملDiscretization Error Analysis for Tikhonov Regularization in Learning Theory
We study the connections between learning from examples and inverse problems. We show that learning from examples can be seen as the discretization of a stochastic inverse problem defined by a Carleman operator. In particular we develop a discretization strategy for this class of inverse problems and we give a convergence analysis. Our approach can be applied to other classes of problems such a...
متن کاملA Regularization Parameter for Nonsmooth Tikhonov Regularization
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...
متن کاملTikhonov Regularization
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 ...
متن کاملAn adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
The aim of this paper is to describe an eecient adaptive strategy for discretizing ill-posed linear operator equations of the rst kind: we consider Tikhonov-Phillips regularization x = (A A + I) ?1 A y with a nite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Analysis and Applications
سال: 2006
ISSN: 0219-5305,1793-6861
DOI: 10.1142/s0219530506000711