Results 21 to 30 of about 48,254 (265)
A SURJECTIVITY PROBLEM FOR MATRICES AND NULL CONTROLLABILITY FOR DIFFERENCE AND DIFFERENTIAL MATRIX EQUATIONS [PDF]
Surveys in Mathematics and its Applications, 2020 Let P be a complex polynomial. We prove that the associated polynomial matrix-valued function \tildeP is surjective if for each λ ∈ ℂ the polynomial P-λ has at least a simple zero. The null controllability for difference and differential matrix equations
Donal O'Regan, Constantin Buşe
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Bounding hermite matrix polynomials
Mathematical and Computer Modelling, 2004 The main object under investigation is the family of the Hermite matrix orthogonal polynomials \(\{H_n(x,A)\}_{n\geq 0}\), which depends on the matrix parameter \(A\) having all its eigenvalues in the open right half plane. The main result (Theorem 1) states that \[ \| H_{2n}(x,A)\| \leq \frac{(2n+1)!
Defez, E. +3 more
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Matrix polynomials with specified eigenvalues
Linear Algebra and its Applications, 2015 This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient matrix. Singular value optimization formulas are derived for these distances facilitating their computation.
Karow, Michael, Mengi, Emre
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Geometry of Matrix Polynomial Spaces [PDF]
Foundations of Computational Mathematics, 2019 Let \(P(\lambda)\) be an \(m \times n\) matrix polynomial defined by \[ P(\lambda) = \lambda^d A_d + \dots + \lambda A_1 +A_0 \] where \(A_i \in {\mathbb C} ^{m\times n}\) for \(i = 0, \dots, d\), and \(A_d \neq 0\). Let \(E(\lambda)\) be an \(m\times n\) matrix polynomial with \(\deg P(\lambda) \ge \deg E(\lambda)\).
Dmytryshyn, Andrii +3 more
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An Implementation of Image Secret Sharing Scheme Based on Matrix Operations
Mathematics, 2022 The image secret sharing scheme shares a secret image as multiple shadows. The secret image can be recovered from shadow images that meet a threshold number.
Zihan Ren, Peng Li, Xin Wang
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Positive semidefinite univariate matrix polynomials [PDF]
Mathematische Zeitschrift, 2018 We study sum-of-squares representations of symmetric univariate real matrix polynomials that are positive semidefinite along the real line. We give a new proof of the fact that every positive semidefinite univariate matrix polynomial of size $n\times n$ can be written as a sum of squares $M=Q^TQ$, where $Q$ has size $(n+1)\times n$, which was recently ...
Hanselka, C., Sinn, R.
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IEEE AccessThis paper presents a scheme that is designed for the effective implementation of lattice reduction for polynomial matrices within the list-decoding algorithm that is applied to the binary Goppa codes.
Ki-Soon Yu, Dae-Woon Lim
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Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree
MathematicsThe estimation of complex natural frequencies in linear systems through their transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs
Raul H. Barroso, Alfonso J. Zozaya Sahad
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Lossy Compression using Adaptive Polynomial Image Encoding
Advances in Electrical and Computer Engineering, 2021 In this paper, an efficient lossy compression approach using adaptive-block polynomial curve-fitting encoding is proposed. The main idea of polynomial curve fitting is to reduce the number of data elements in an image block to a few coefficients.
OTHMAN, S. +3 more
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ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS
Ural Mathematical Journal, 2023 Let \(\mathbb{C}^{m\times m}\) be the set of all \(m\times m\) matrices whose entries are in \(\mathbb{C},\) the set of complex numbers. Then \(P(z):=\sum\limits_{j=0}^nA_jz^j,\) \(A_j\in \mathbb{C}^{m\times m},\) \(0\leq j\leq n\) is called a matrix ...
Zahid Bashir Monga, Wali Mohammad Shah
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