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

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Persistent URL	http://purl.org/net/epubs/work/43525216
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Record Id	43525216
Title	Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation
Contributors	I Dauzickaite, AS Lawless, JA Scott (STFC Rutherford Appleton Lab.), PJ van Leeuwen
Abstract	We consider the large-sparse symmetric linear systems of equations that arise in the solution of weak constraint four-dimensional variational data assimilation. 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 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.
Organisation	STFC , SCI-COMP
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Funding Information
Related Research Object(s):	46609636
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	RAL Preprints RAL-P-2019-004, Numer Linear Algebr STFC, 2019.		RAL-P-2019-004.pdf	2019