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Neurons have an inherent capability to learn order relations: A theoretical foundation that explains numerous experimental data

Yang Y, Maass W.
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TOEPLITZ BASES IN MATRIX FIELDS

Analysis, 1988
The authors establish several criteria in order that the family of unit vectors \((e^ k)_{k\geq 1}\) should be a Toeplitz T-basis in a matrix field \(E_ A\), where T is a lower triangular matrix and E is a BK-space. Firstly, they give a characterization theorem in general hypotheses.
Jakimovski, Amnon, Russell, Dennis, Stieglitz, Michael   +2 more
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Efficient inversion of Toeplitz-block Toeplitz matrix

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1983
An iterative algorithm for the inversion of a Toeplitz-block Toeplitz matrix consisting of \(m\times m\) blocks of size \(p\times p\) is described. The algorithm presented exploits the spectrum of the Toeplitz-block Toeplitz matrix and outperforms \textit{H. Akaike}'s algorithm [see SIAM J. Appl. Math. 24, 234-241 (1973; Zbl 0234.65039)] by a factor of
Wax, Mati, Kailath, Thomas
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Matrix rigidity of random Toeplitz matrices

computational complexity, 2016
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Goldreich, Oded, Tal, Avishay
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A Hermitian Toeplitz matrix is unitarily similar to a real Toeplitz-plus-Hankel matrix

IEEE Transactions on Signal Processing, 1991
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Wilkes, D. M., Morgera, S. D., Noor, F., Hayes, M. H. III   +3 more
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Block Toeplitz Matrix Inversion

SIAM Journal on Applied Mathematics, 1973
An iterative procedure for the inversion of a block Toeplitz matrix is given. Hitherto published procedures are obtained as special cases of the present procedure. The use of the procedure in time series analysis is briefly explained.
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Toeplitz Jacobian Matrix for Nonlinear Periodic Vibration

Journal of Applied Mechanics, 1995
The main difference between a linear system and a nonlinear system is in the non-uniqueness of solutions manifested by the singular Jacobian matrix. It is important to be able to express the Jacobian accurately, completely, and efficiently in an algorithm to analyze a nonlinear system.
Leung, A. Y. T., Ge, T.
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A symmetric rank-revealing toeplitz matrix decomposition

Journal of VLSI signal processing systems for signal, image and video technology, 1996
Summary: In signal and image processing, regularization often requires a rank-revealing decomposition of a symmetric Toeplitz matrix with a small rank deficiency. In this paper, we present an efficient factorization method that exploits symmetry as well as the rank and Toeplitz properties of the given matrix.
Luk, Franklin T., Qiao, Sanzheng
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From matrix polynomial to determinant of block Toeplitz–Hessenberg matrix

Numerical Algorithms, 2023
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