Results 11 to 20 of about 543,835 (181)
Random Perturbations of Matrix Polynomials [PDF]
Journal of Theoretical Probability, 2020 AbstractA sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of the resolvent of the sum is derived, and the eigenvalues are localised.
Patryk Pagacz, Michał Wojtylak
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IET Control Theory & Applications, 2023 The problem of the singular Roesser (state‐space) model realization of non‐causal multivariate transfer (function) matrices is investigated. Specifically, the notion of so‐called admissible transformation is introduced, which allows to introduce and ...
Dongdong Zhao +5 more
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Matrix-Valued Gegenbauer-Type Polynomials [PDF]
Constructive Approximation, 2017 Matrix-valued Gegenbauer-type polynomials are investigated. The main results of the paper are stated in Sections 2 and 3. In Section 2 the matrix-valued weight functions \(W^{(\nu)}(x)\), which are analogues of the weight function for the Gegenbauer polynomials \(C^{(\nu)}_n(x)\) are introduced: \(W^{(\nu)}(x)= (1-x^2)^{\nu-1/2}W^{(\nu)}_{\mathrm{pol}}(
Koelink, Erik +2 more
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Matrix of Polynomials Model based Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling [PDF]
, 2017 We study the problem of dictionary learning for signals that can be represented as polynomials or polynomial matrices, such as convolutive signals with time delays or acoustic impulse responses.
Dong, Jing +4 more
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Shortening the order of paraunitary matrices in SBR2 algorithm [PDF]
, 2007 The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the ...
Ta, C.H., Weiss, S.
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Matrix approach to solve polynomial equations
Results in Applied Mathematics, 2023 Polynomials are widely employed to represent numbers derived from mathematical operations in nearly all areas of mathematics. The ability to factor polynomials entirely into linear components allows for a wide range of problem simplifications. This paper
Samir Brahim Belhaouari +2 more
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IEEE Access, 2020 In this paper, new conditions of the stability, stabilization and L2-gain performance of periodic piecewise systems are proposed. Both the continuous and discontinuous Lyapunov functions with dwell-time related time-varying Lyapunov matrix polynomial are
Panshuo Li +3 more
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Efficient Evaluation of Matrix Polynomials beyond the Paterson–Stockmeyer Method
Mathematics, 2021 Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson–Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically by the total number of matrix ...
Jorge Sastre, Javier Ibáñez
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Matrix Valued Laguerre Polynomials [PDF]
, 2019 20 pages, to appear in Positivity and Noncommutative Analysis Festschrift in Honour of Ben de Pagter (eds. G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven and A. Wickstead)
Koelink, H.T., Roman, P.M.
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List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes [PDF]
, 2012 A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are
F. Hernando +15 more
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