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

Dauzickaite, L., Lawless, A., Scott, J. 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. ISSN 1099-1506

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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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO)
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:90731
Publisher:Wiley

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