Displacement Structures of Covariance Matrices, Lossless Systems, and Numerical Algorithm Design
Copyright policy )Displacement Structures of Covariance Matrices, Lossless Systems, and Numerical Algorithm Design
The displacement rank theory of \textit{T. Kailath, S.-Y. Kung} and \textit{M. Morf} [J. Math. Anal. Appl. 68, 395-407 (1979; Zbl 0433.15001)] has played a key role in the development of fast computational algorithms for structured covariance matrices. Many of these fast algorithms are known to be unstable. This paper, which contains a substantial review of recent literature on the subject, highlights the role of backward error analysis in the design of stable fast algorithms. Applications to signal processing are also discussed.
Signal theory (characterization, reconstruction, filtering, etc.), Numerical solutions to overdetermined systems, pseudoinverses, General systems theory, displacement rank, Other matrix algorithms, fast computational algorithms, backward error analysis, structured covariance matrices, signal processing
Signal theory (characterization, reconstruction, filtering, etc.), Numerical solutions to overdetermined systems, pseudoinverses, General systems theory, displacement rank, Other matrix algorithms, fast computational algorithms, backward error analysis, structured covariance matrices, signal processing
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