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Résumé
The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed. The aim is to investigate from a theoretical point of view the inefficiencies of this approach as observed in the application of the weakly constrained 4D-Var algorithm in geosciences. Bounds on the eigenvalues of the preconditioned system matrix are provided. It highlights the interplay of the eigenstructures of both the model and weighting matrices: maintaining a low bound on the eigenvalues of the preconditioned system matrix requires an approximation error of the model matrix which compensates for the condition number of the weighting matrix. A low-dimension analytical example is given illustrating the resulting potential inefficiency of such preconditioners. The consequences of these results in the context of the state formulation of the weakly constrained 4D-Var data assimilation problem are discussed. It is shown that the common approximations of the tangent linear model which maintain parallelization-in-time properties (identity or null matrix) can result in large bounds on the eigenvalues of the preconditioned matrix system.
langue originale | Anglais |
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Pages (de - à) | 934-940 |
Nombre de pages | 7 |
journal | Quarterly Journal of the Royal Meteorological Society |
Volume | 144 |
Numéro de publication | 712 |
Les DOIs | |
Etat de la publication | Publié - avr. 2018 |
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ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
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A primal-dual approach of weak-constrained variational data assimilation: (Iterate) History matters
Philippe Toint (Orateur)
13 oct. 2017Activité: Types de discours ou de présentation › Discours invité