2009/10/13 by Yury Podlipenko, Podlipenko, Yury, Yury Shestopalov +4
Computer Science · Mathematics · #35J25 #45Fxx #45Kxx #49xx 93E10 (Primary) #78M50 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Statistical and numerical algorithms #math.AP #math.OC #msc:35J25 #msc:45Fxx #msc:45Kxx #msc:49xx #msc:78M50 #msc:93E10
paper · pdf · doi:10.48550/arxiv.0910.2331
93 pages
arxiv created 2009/10/13 · openalex publication_date 2009/10/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the determination of minimax estimates is reduced to the solution of integro-differential equations in bounded domains. When observations are distributed on a system of surfaces the problem is reduced to solving integral equations on an unclosed bounded surface which is a union of the boundary of the domain and this system of surfaces. Minimax estimation of the solutions to the boundary value problems from point observations is also studied.