Estimation under uncertainties of acoustic and electromagnetic fields from noisy observations

Details Estimation under uncertainties of acoustic and electromagnetic fields from noisy observations Estimation under uncertainties of acoustic and electromagnetic fields from noisy observations

2009-10-13

arxiv.org/abs/0910.2331v1

Mathematics

Analysis of PDEs

93 pages

Scientific paper

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.

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