Geodesic
Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems
Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 675-687 
E. V. Vasil'eva. Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems. Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 675-687. http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a3/
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     author = {E. V. Vasil'eva},
     title = {Lower {Bounds} for the {Rate} of {Convergence} of {Dynamic} {Reconstruction} {Algorithms} for {Distributed-Parameter} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {675--687},
     year = {2004},
     volume = {76},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain lower bounds for the rate of convergence of reconstruction algorithms for distributed-parameter systems of parabolic type. In the case of a pointwise constraint on control for known reconstruction algorithms, we establish a lower bound on the rate of convergence, which shows that, given certain conditions, for each solution of the system one can choose such a collection of measurements so that the reconstruction error will not be less than a certain value. In the case of unbounded controls, we obtain lower bounds for a possible reconstruction error for each trajectory as well as for a given set of trajectories. For a system of special form, we construct an algorithm for which we obtain upper and lower bounds for accuracy having identical order for a specific choice of matching of the parameters.

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