Generalized sentinels defined via least squares

Guy Chavent 1
Abstract : We address the problem of monitoring a linear functional (c,x)E of an Hilbert space E, the available data being the observation z, in an Hilbert space F, of a vector Ax depending linearly of x through some known operator A # (E,F). When E = E1 x E2, c = (c1,0) and A is injective and defined through the solution of a partial differential equation, J.L. Lions (1988,1990) introduced sentinels s F such that (s, Ax)F is sensitive to x1 E1 but insensitive to x2 E2. In this paper, we prove the existence, in the general of a generalized sentinel (s,n) F x E, where F F with F dense in F, such that for any a priori guess xo of x, one has : < s, Ax >TFF + (n, xo)E =(c, x)E where x is the least squares estimates of x closest to xo, and a family of regularized sentinels (sn, nn) F x E which converge to (s,n). Generalized sentinels unify the least square approach (by construction !) and the sentinel approach (when A is injective) and provide a general frame work for the construction of "sentinels with special sensitivity" in the sense of J.L. Lions (1990).
Type de document :
[Research Report] RR-1932, INRIA. 1993
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Soumis le : mercredi 24 mai 2006 - 16:12:57
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : mardi 12 avril 2011 - 18:48:58



  • HAL Id : inria-00074742, version 1



Guy Chavent. Generalized sentinels defined via least squares. [Research Report] RR-1932, INRIA. 1993. 〈inria-00074742〉



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