The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Toeplitz and Circulant Matrices: A Review
Abstract
Toeplitz and Circulant Matrices: A review derives in a tutorial manner the fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements. 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. Toeplitz and Circulant Matrices: A review is written for students and practicing engineers in an accessible manner bringing this important topic to a wider audience.
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Cites
Principles of mathematical analysis
Rudin, W. (1964) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 5,195
Elements of Information Theory
Jacobs, K. (1992) · Discrete Stochastics · doi:10.1007/978-3-0348-8645-1_7 · Cited by 2,918
Toeplitz Forms and Their Applications
Grenander, U., & Szego, G. (1958) · University of California Press eBooks · doi:10.1525/9780520355408 · Cited by 1,526
Rate Distortion Theory: A Mathematical Basis for Data Compression
Davisson, L. (1972) · IEEE Transactions on Communications · doi:10.1109/tcom.1972.1091311 · Cited by 895
On the asymptotic eigenvalue distribution of Toeplitz matrices
Gray, R. (1972) · IEEE Transactions on Information Theory · doi:10.1109/tit.1972.1054924 · Cited by 526
Self-citationA unifying approach to some old and new theorems on distribution and clustering
Tyrtyshnikov, E. E. (1996) · Linear Algebra and its Applications · doi:10.1016/0024-3795(94)00025-5 · Cited by 327
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Bartlett, M. S., Grenander, U., & Rosenblatt, M. (1957) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343106 · Cited by 313
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Exploiting the Circulant Structure of Tracking-by-Detection with Kernels
Henriques, J. F., Caseiro, R., Martins, P., & Batista, J. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-33765-9_50 · Cited by 2,310
Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling
Duchi, J. C., Agarwal, A., & Wainwright, M. J. (2012) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2011.2161027 · Cited by 947
Image data compression: A review
Jain, A. K. (1981) · Proceedings of the IEEE · doi:10.1109/proc.1981.11971 · Cited by 709
On Distributed Averaging Algorithms and Quantization Effects
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Metadata
- Authors
- Gray, R. M.
- Venue
- now publishers, Inc. eBooks
- Publisher
- now Publishers Inc
- Published
- 2005
- OpenAlex
- W4243833160
- Cited by
- 759
- References
- 7
- FWCI
- 5.79
- Type
- book
- Language
- en
- Open access
- closed
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