Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation |
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Authors: | Ieva
Dauickait Amos S Lawless Jennifer A Scott Peter Jan van Leeuwen |
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Institution: | Ieva
Dau?ickait?,Amos S. Lawless,Jennifer A. Scott,Peter Jan van Leeuwen |
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Abstract: | 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 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, 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. |
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Keywords: | data assimilation saddle point systems sparse linear systems spectral estimates weak constraint 4D‐Var |
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