Results 31 to 40 of about 2,914,259 (200)
Biorthogonal matrix polynomials related to Jacobi matrix polynomials
Computers & Mathematics with Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Varma, Serhan, Taşdelen, Fatma
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Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade [PDF]
, 2017 We show that the set of m×m complex skew-symmetric matrix polynomials of odd grade d, i.e., of degree at most d, and (normal) rank at most 2r is the closure of the single set of matrix polynomials ...
Andrii Dmytryshyn, F. Dopico
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A Framework for Structured Linearizations of Matrix Polynomials in Various Bases [PDF]
SIAM Journal on Matrix Analysis and Applications, 2016 We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework provides an extension
L. Robol, R. Vandebril, P. Dooren
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Matrix Approaches for Gould–Hopper–Laguerre–Sheffer Matrix Polynomial Identities
Axioms, 2023 The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques.
Tabinda Nahid +2 more
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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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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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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 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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Mathematics, 2015 The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
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