An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An 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 کامل

A 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 کامل

Data Based Regularization Matrices for the Tikhonov-Phillips Regularization

In Tikhonov-Phillips regularization of general form the given ill-posed linear system is replaced by a Least Squares problem including a minimization of the solution vector x, relative to a seminorm ‖Lx‖2 with some regularization matrix L. Based on the finite difference matrix Lk, given by a discretization of the first or second derivative, we introduce the seminorm ‖LkD x̃ x‖2 where the diagona...

متن کامل

On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems

In the study of the choice of the regularization parameter for Tikhonov regularization of nonlinear ill-posed problems, Scherzer, Engl and Kunisch proposed an a posteriori strategy in 1993. To prove the optimality of the strategy, they imposed many very restrictive conditions on the problem under consideration. Their results are difficult to apply to concrete problems since one can not make sur...

متن کامل

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 کامل

ذخیره 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: Numerische Mathematik

سال: 2001

ISSN: 0029-599X

DOI: 10.1007/pl00005421