# Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation

Dauzickaite, I., Lawless, A. S., Scott, J. A. and Van Leeuwen, P. J. (2020) Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation. Numerical Linear Algebra with Applications, 27 (5). ISSN 1099-1506

 Preview
Text (Open Access) - Published Version

1MB
Text - Accepted Version
· Restricted to Repository staff only

2MB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1002/nla.2313

## Abstract/Summary

We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a $3 \times 3$ block structure but block eliminations can be performed to reduce them to saddle point systems with a $2 \times 2$ block structure, or further to symmetric positive definite systems. In this paper, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.

Item Type: Article Yes Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO)Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and StatisticsScience > School of Mathematical, Physical and Computational Sciences > Department of Meteorology 90731 Wiley