Projects per year
Abstract
The effect of preconditioning linear weighted leastsquares 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 4DVar 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 lowdimension 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 4DVar data assimilation problem are discussed. It is shown that the common approximations of the tangent linear model which maintain parallelizationintime properties (identity or null matrix) can result in large bounds on the eigenvalues of the preconditioned matrix system.
Original language  English 

Pages (fromto)  934940 
Number of pages  7 
Journal  Quarterly Journal of the Royal Meteorological Society 
Volume  144 
Issue number  712 
DOIs  
Publication status  Published  Apr 2018 
Keywords
 linear leastsquares
 preconditioning
 data assimilation
 weaklyconstrained 4DVar
 earth sciences
Fingerprint Dive into the research topics of 'A note on preconditioning weighted linear leastsquares with consequences for weakly constrained variational data assimilation'. Together they form a unique fingerprint.
Projects
 1 Active
Activities
 1 Invited talk

A primaldual approach of weakconstrained variational data assimilation: (Iterate) History matters
Philippe Toint (Speaker)
13 Oct 2017Activity: Talk or presentation types › Invited talk