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Fast Computation of the Matrix Exponential for a Toeplitz Matrix [PDF]
SIAM Journal on Matrix Analysis and Applications, 2018 The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured $n\times n$ matrix it can be computed in $\mathcal{O}(n^3)$ operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for example as the result of discretizing integral equations with a time invariant ...
Daniel Kressner, Robert Luce
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Matrix Representations of Asymmetric Truncated Toeplitz Operators [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2020 AbstractIn this paper, we describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces$$K_1$$K1and$$K_2$$K2. The novelty of our approach is that here we consider matrix representations computed with respect to bases of different type in$$K_1$$K1and$$K_2$$K2(for example, kernel basis ...
Joanna Jurasik, Bartosz Łanucha
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Toeplitz matrix completion via a low-rank approximation algorithm [PDF]
Journal of Inequalities and Applications, 2020 In this paper, we propose a low-rank matrix approximation algorithm for solving the Toeplitz matrix completion (TMC) problem. The approximation matrix was obtained by the mean projection operator on the set of feasible Toeplitz matrices for every ...
Ruiping Wen, Yaru Fu
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An Underwater Velocity-Independent DOA Estimation Based on Improved Toeplitz Matrix Reconstruction [PDF]
SensorsConventional acoustic velocity-independent direction of arrival (DOA) estimation models have limited measurement ranges and low degrees of freedom.
Xuejin Zhao +3 more
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A Low-Complexity Quantum Simulation Framework for Toeplitz-Structured Matrix and Its Application in Signal Processing [PDF]
IEEE Transactions on Quantum Engineering, 2023 Toeplitz matrix reconstruction algorithms (TMRAs) are one of the central subroutines in array processing for wireless communication applications. The classical TMRAs have shown excellent accuracy in the spectral estimation for both uncorrelated and ...
Mostafizur Rahaman Laskar +2 more
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Source Enumeration via Toeplitz Matrix Completion [PDF]
ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020 This paper addresses the problem of source enumeration by an array of sensors in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances, referred to non-iid noise hereafter, when the sources are uncorrelated.
Vaibhav Garg +3 more
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Two fast algorithms for finding the solution of the lower Hessenberg quasi-Toeplitz linear system from Markov chain [PDF]
Scientific ReportsWe present two fast algorithms for finding the solution of the nonsingular lower Hessenberg quasi-Toeplitz linear system stem from Markov chain. And we confirm the complexity of these two algorithms is both O $$(n\log n)$$ based on the fact that a lower ...
Yaru Fu +3 more
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FIXED POINT THEOREM FOR AN INFINITE TOEPLITZ MATRIX [PDF]
Bulletin of the Australian Mathematical Society, 2020 AbstractFor an infinite Toeplitz matrix T with nonnegative real entries we find the conditions under which the equation $\boldsymbol {x}=T\boldsymbol {x}$ , where $\boldsymbol {x}$ is an infinite vector column, has a nontrivial bounded positive solution.
Vyacheslav M. Abramov
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Product of matrix valued truncated Toeplitz operators
Hacettepe Journal of Mathematics and Statistics, 2022 Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication operator to the vector valued model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is a matrix valued non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that the product $A_\Phi A_\Psi$ is itself a ...
Muhammad Ahsan Khan
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Combined Matrix of a Tridiagonal Toeplitz Matrix
AxiomsIn this work, combined matrices of tridiagonal Toeplitz matrices are studied. The combined matrix is known as the Relative Gain Array in control theory.
Begoña Cantó +2 more
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