A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation
arXiv:1709.09031 · doi:10.1002/qj.3262
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.
10 pages, 2 figures