Geodesic
Minimax state estimates for abstract Neumann problems
Minimax theory and its applications, Tome 3 (2018) no. 1
Cet article a éte moissonné depuis la source Minimax Theory and its Applications website

Voir la notice de l'article

The paper presents analytic expressions of minimax (worst-case) estimates for solutions of linear abstract Neumann problems in Hilbert space with uncertain (not necessarily bounded!) inputs and boundary conditions given incomplete observations with stochastic noise. The latter is assumed to have uncertain but bounded correlation operator. It is demonstrated that the minimax estimate is asymptotically exact under mild assumptions on the observation operator and the bounding sets. A relationship between the proposed estimates and a robust pseudo-inversion of compact operators is revealed. This relationship is demonstrated on an academic numerical example: homogeneous Neumann problem for Poisson equation in two spatial dimensions.
Mots-clés : Minimax, filtering, linear operator equations, Neumann problems, pseudo-inversion, differentiation 
@article{MTA_2018_3_1_a5,
     author = {Sergiy Zhuk and Olexander Nakonechnii},
     title = {Minimax state estimates for abstract {Neumann} problems},
     journal = {Minimax theory and its applications},
     year = {2018},
     volume = {3},
     number = {1},
     zbl = {1384.93052},
     url = {http://geodesic.mathdoc.fr/item/MTA_2018_3_1_a5/}
}
TY  - JOUR
AU  - Sergiy Zhuk
AU  - Olexander Nakonechnii
TI  - Minimax state estimates for abstract Neumann problems
JO  - Minimax theory and its applications
PY  - 2018
VL  - 3
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MTA_2018_3_1_a5/
ID  - MTA_2018_3_1_a5
ER  - 
%0 Journal Article
%A Sergiy Zhuk
%A Olexander Nakonechnii
%T Minimax state estimates for abstract Neumann problems
%J Minimax theory and its applications
%D 2018
%V 3
%N 1
%U http://geodesic.mathdoc.fr/item/MTA_2018_3_1_a5/
%F MTA_2018_3_1_a5
Sergiy Zhuk; Olexander Nakonechnii. Minimax state estimates for abstract Neumann problems. Minimax theory and its applications, Tome 3 (2018) no. 1. http://geodesic.mathdoc.fr/item/MTA_2018_3_1_a5/