### Abstract

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.

Language | English |
---|---|

Number of pages | 10 |

Journal | Quarterly Journal of the Royal Meteorological Society |

State | Accepted/In press - 2018 |

### Fingerprint

### Keywords

- linear least-squares
- preconditioning
- data assimilation
- weakly-constrained 4D-Var
- earth sciences

### Cite this

}

**A note on preconditioning weighted linear least-squares with consequences for weakly constrained variational data assimilation.** / Gratton, Serge; Selime, Gürol; Simon, Ehouarn; Toint, Philippe.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A note on preconditioning weighted linear least-squares with consequences for weakly constrained variational data assimilation

AU - Gratton,Serge

AU - Selime,Gürol

AU - Simon,Ehouarn

AU - Toint,Philippe

PY - 2018

Y1 - 2018

N2 - The effect of preconditioning linear weighted least-squares using anapproximation of the model matrix is analyzed, showing the interplay of theeigenstructures of both the model and weighting matrices. A small example isgiven illustrating the resulting potential inefficiency of suchpreconditioners. Consequences of these results in the context of theweakly-constrained 4D-Var data assimilation problem are finally discussed.

AB - The effect of preconditioning linear weighted least-squares using anapproximation of the model matrix is analyzed, showing the interplay of theeigenstructures of both the model and weighting matrices. A small example isgiven illustrating the resulting potential inefficiency of suchpreconditioners. Consequences of these results in the context of theweakly-constrained 4D-Var data assimilation problem are finally discussed.

KW - linear least-squares

KW - preconditioning

KW - data assimilation

KW - weakly-constrained 4D-Var

KW - earth sciences

M3 - Article

JO - Quarterly Journal of the Royal Meteorological Society

T2 - Quarterly Journal of the Royal Meteorological Society

JF - Quarterly Journal of the Royal Meteorological Society

SN - 0035-9009

ER -