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
Number of pages10
JournalQuarterly Journal of the Royal Meteorological Society
StateAccepted/In press - 2018

Fingerprint

Data Assimilation
Linear Least Squares
Weighted Least Squares
Matrix Models
Preconditioning
data assimilation
Preconditioner
Weighting
matrix
Approximation
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.",
keywords = "linear least-squares, preconditioning, data assimilation, weakly-constrained 4D-Var, earth sciences",
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language = "English",
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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 -