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Toeplitz and circulant matrices
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TLDR
The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toepler matrices with absolutely summable elements are derived in a tutorial manner in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject.Abstract:
The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.read more
Citations
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Journal ArticleDOI
High-Speed Tracking with Kernelized Correlation Filters
TL;DR: A new kernelized correlation filter is derived, that unlike other kernel algorithms has the exact same complexity as its linear counterpart, which is called dual correlation filter (DCF), which outperform top-ranking trackers such as Struck or TLD on a 50 videos benchmark, despite being implemented in a few lines of code.
Journal ArticleDOI
Spectrum analysis—A modern perspective
Steven Kay,S.L. Marple +1 more
TL;DR: In this paper, a summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented, including classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods.
The Matrix Cookbook
TL;DR: Theodorakopoulos et al. as mentioned in this paper used the Oticon Foundation for funding their PhD studies, and they would like to thank the following for contributions and suggestions: Bill Baxter, Brian Templeton, Christian Rishoj, Christian Schroppel Douglas L. Theobald, Esben Hoegh-Rasmussen, Glynne Casteel, Jan Larsen, Jun Bin Gao, Jurgen Struckmeier, Kamil Dedecius, Korbinian Strimmer, Lars Christiansen, Lars Kai Hansen, Leland Wilkinson, Lig
Journal ArticleDOI
The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)
Book ChapterDOI
Exploiting the circulant structure of tracking-by-detection with kernels
TL;DR: Using the well-established theory of Circulant matrices, this work provides a link to Fourier analysis that opens up the possibility of extremely fast learning and detection with the Fast Fourier Transform, which can be done in the dual space of kernel machines as fast as with linear classifiers.
References
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Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
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The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book
Principles of mathematical analysis
TL;DR: The real and complex number system as discussed by the authors is a real number system where the real number is defined by a real function and the complex number is represented by a complex field of functions.