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arXiv · 1709.09031

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

Serge Gratton·Selime Gürol·Ehouarn Simon·Philippe L. Toint
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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.

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Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe L. Toint. 2017-09-26. A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation. https://doi.org/10.1002/qj.3262

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