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• W4387362019 abstract "Abstract Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced truncation has been drawn (Qian et al in Sci Comput 91:29, 2022). Although this connection is new, the application of balanced truncation to data assimilation is not a novel idea: it has already been used in four-dimensional variational data assimilation (4D-Var). This paper discusses the application of balanced truncation to linear Gaussian Bayesian inference, and, in particular, the 4D-Var method, thereby strengthening the link between systems theory and data assimilation further. Similarities between both types of data assimilation problems enable a generalisation of the state-of-the-art approach to the use of arbitrary prior covariances as reachability Gramians. Furthermore, we propose an enhanced approach using time-limited balanced truncation that allows to balance Bayesian inference for unstable systems and in addition improves the numerical results for short observation periods." @default.
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• W4387362019 date "2023-10-05" @default.
• W4387362019 modified "2023-10-06" @default.
• W4387362019 title "Time-Limited Balanced Truncation for Data Assimilation Problems" @default.
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• W4387362019 doi "https://doi.org/10.1007/s10915-023-02358-4" @default.
• W4387362019 hasPublicationYear "2023" @default.
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