A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation
Numerical Analysis
2021-05-31 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1709.09031,
title = {A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation},
author = {Serge Gratton and Selime Gürol and Ehouarn Simon and Philippe L. Toint},
journal= {arXiv preprint arXiv:1709.09031},
year = {2021}
}
Comments
10 pages, 2 figures