Research output per year
Research output per year
Serge Gratton, Gürol Selime, Ehouarn Simon, Philippe Toint
Research output: Contribution to journal › Article › peer-review
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.
Original language | English |
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Pages (from-to) | 934-940 |
Number of pages | 7 |
Journal | Quarterly Journal of the Royal Meteorological Society |
Volume | 144 |
Issue number | 712 |
DOIs | |
Publication status | Published - Apr 2018 |
Research output: Contribution to journal › Article › peer-review
Research output: Working paper
Research output: Contribution to journal › Article › peer-review
Philippe Toint (Speaker)
Activity: Talk or presentation types › Invited talk