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

Ehouarn Simon; Philippe L. Toint; Selime G\"urol; Serge Gratton

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

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arxiv 1709.09031 v1 pith:CBCXNYCN submitted 2017-09-26 math.NA cs.NAmath.OC

Serge Gratton , Selime Gürol , Ehouarn Simon , Philippe L. Toint This is my paper · ORCID

classification math.NAcs.NAmath.OC

keywords assimilationconsequencesdatalinearmodelpreconditioningweakly-constrainedweighted

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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.

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