Discretization of variational regularization in Banach spaces
نویسندگان
چکیده
منابع مشابه
Discretization of variational regularization in Banach spaces
Consider a nonlinear ill-posed operator equation F (u) = y where F is defined on a Banach space X. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data. As shown in the literature, depending on the setting, convergence of the regularized solutions of the finite dimensional problems can be with respect to the stro...
متن کاملHanke-Raus heuristic rule for variational regularization in Banach spaces
We generalize the heuristic parameter choice rule of Hanke-Raus for quadratic regularization to general variational regularization for solving linear as well as nonlinear ill-posed inverse problems in Banach spaces. Under source conditions formulated as variational inequalities, we obtain a posteriori error estimates in term of Bregman distance. By imposing certain conditions on the random nois...
متن کاملFuzzy Multivalued Variational Inclusions in Banach Spaces
The purpose of this paper is to introduce the concept of general fuzzy multivalued variational inclusions and to study the existence problem and the iterative approximation problem for certain fuzzy multivalued variational inclusions in Banach spaces. Using the resolvent operator technique and a new analytic technique, some existence theorems and iterative approximation techniques are presented...
متن کاملGeneralized System of Variational Inequalities in Banach Spaces
In this paper, we introduce and consider a new system of extended general variational inequalities in Banach spaces. We establish the equivalence between the extended general variational inequalities and the fixed point problems. We use this equivalent formulation to suggest some iterative methods for solving this new system. We prove the convergence analysis of the proposed iterative methods u...
متن کاملMixed Tikhonov regularization in Banach spaces based on domain decomposition
We analyze Tikhonov regularization where the forward operator is defined on a direct sum U of several Banach spaces U i ; i ¼ 1;. .. ; m. The regularization term on U is a sum of different regularizations on each U i. The theoretical framework, known for the case m ¼ 1, can be easily reformulated to the case m > 1. Under certain assumptions on weak topologies and on the forward operator it is p...
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: Inverse Problems
سال: 2010
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/26/10/105017