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A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation

Serge Gratton(serge.gratton***at***enseeiht.fr)
Selime Gürol(selime.gurol***at***cerfacs.fr)
Ehouarn Simon(ehouarn.simon***at***enseeiht.fr)
Philippe Toint(philippe.toint***at***unamur.be)

Abstract: The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the weakly-constrained 4D-Var data assimilation problem are finally discussed.

Keywords: weighted least-squares, data assimilation, preconditioning

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Applications -- Science and Engineering (Basic Sciences Applications )

Citation: naXys Technical report, naXys, University of Namur, Namur, Belgium, 2017

Download: [PDF]

Entry Submitted: 09/26/2017
Entry Accepted: 09/26/2017
Entry Last Modified: 09/26/2017

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