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Companion matrices and their relations to Toeplitz and Hankel matrices [PDF]
Special Matrices, 2015 In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing ...
Luo Yousong, Hill Robin
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Special Matrices, 2020 In this paper, our main attention is paid to calculate the determinants and inverses of two types Toeplitz and Hankel tridiagonal matrices with perturbed columns.
Fu Yaru +3 more
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The smallest eigenvalue of large Hankel matrices [PDF]
Applied Mathematics and Computation, 2018 19 pages, 4 ...
Mengkun Zhu, , Niall Emmart
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Generalized Data–Driven Predictive Control: Merging Subspace and Hankel Predictors
Mathematics, 2023 Data–driven predictive control (DPC) is becoming an attractive alternative to model predictive control as it requires less system knowledge for implementation and reliable data is increasingly available in smart engineering systems.
M. Lazar, P. C. N. Verheijen
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Analytical solutions to some generalized and polynomial eigenvalue problems
Special Matrices, 2021 It is well-known that the finite difference discretization of the Laplacian eigenvalue problem −Δu = λu leads to a matrix eigenvalue problem (EVP) Ax =λx where the matrix A is Toeplitz-plus-Hankel.
Deng Quanling
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Mixed Alternating Projections with Application to Hankel Low-Rank Approximation
Algorithms, 2022 The method of alternating projections for extracting low-rank signals is considered. The problem of decreasing the computational costs while keeping the estimation accuracy is analyzed.
Nikita Zvonarev, Nina Golyandina
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Stable factorization for Hankel and Hankel‐like matrices [PDF]
Numerical Linear Algebra with Applications, 2001 AbstractThis paper gives fast O(n2) algorithms for the factorization of positive‐definite and indefinite Hankel matrices. The algorithms are based on the concept of displacement structure and are valid for the more general class of Hankel‐like matrices. The positive‐definite algorithm is proven to be backward stable.
Vadim Olshevsky, Michael Stewart 0005
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Perturbations on the antidiagonals of Hankel matrices [PDF]
Applied Mathematics and Computation, 2013 Given a strongly regular Hankel matrix, and its associated sequence of moments whichdefines a quasi-definite moment linear functional, we study the perturbation of a fixedmoment, i.e., a perturbation of one antidiagonal of the Hankel matrix. We define a linearfunctional whose action results in such a perturbation and establish necessary and ...
Kenier Castillo +3 more
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On the spectral properties of real antitridiagonal Hankel matrices
Special Matrices, 2022 In this article, we express the eigenvalues of real antitridiagonal Hankel matrices as the zeros of given rational functions. We still derive eigenvectors for these structured matrices at the expense of prescribed eigenvalues.
Lita da Silva João
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On Determinantal Varieties of Hankel Matrices [PDF]
Algebra, 2014 Let ℌ be a class of n×n Hankel matrices HA whose entries, depending on a given matrix A, are linear forms in n variables with coefficients in a finite field 𝔽q. For every matrix in ℌ, it is shown that the varieties specified by the leading minors of orders from 1 to n-1 have the same number qn-1 of points in 𝔽qn.
Edoardo Ballico, Michele Elia
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