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

Serge Gratton, Gürol Selime, Ehouarn Simon, Philippe Toint

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages934-940
JournalQuarterly Journal of the Royal Meteorological Society
Volume144
Issue number172
Publication statusPublished - Apr 2018

Fingerprint

Data Assimilation
Linear Least Squares
Weighted Least Squares
Matrix Models
Preconditioning
data assimilation
Weighting
matrix
Model
Context
effect

Keywords

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

Cite this

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

In: Quarterly Journal of the Royal Meteorological Society, Vol. 144, No. 172, 04.2018, p. 934-940.

Research output: Contribution to journalArticle

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AU - Selime, Gürol

AU - Simon, Ehouarn

AU - Toint, Philippe

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KW - linear least-squares

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KW - earth sciences

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