Results 41 to 50 of about 2,914,259 (200)
Analytical properties of the two-variables Jacobi matrix polynomials with applications
Demonstratio Mathematica, 2021 In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived.
Abdalla Mohamed, Hidan Muajebah
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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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Linearizations of matrix polynomials in Newton bases
Linear Algebra and its Applications, 2018 We discuss matrix polynomials expressed in a Newton basis, and the associated polynomial eigenvalue problems. Properties of the generalized ansatz spaces associated with such polynomials are proved directly by utilizing a novel representation of ...
Vasilije Perović, D. Mackey
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On vector spaces of linearizations for matrix polynomials in orthogonal bases [PDF]
, 2016 Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential linearizations for P ...
H. Faßbender, Philip Saltenberger
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Extended biorthogonal matrix polynomials [PDF]
Mathematica Moravica, 2017 The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and ...
Ayman Shehata
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Symmetric Linearizations for Matrix Polynomials [PDF]
SIAM Journal on Matrix Analysis and Applications, 2007 The aim of this paper is to gain new insight into the vector spaces of pencils \({\mathbf L}_1(P)\) and \({\mathbf L}_2(P)\), and their intersection \(\text{DL}(P)\), that arise in connection with the linearization of the polynomial eigenvalue problem \(P(\lambda)x = 0\).
Higham, Nicholas J. +3 more
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Finding identities and q-difference equations for new classes of bivariate q-matrix polynomials
Applied Mathematics in Science and EngineeringThis article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the ...
Subuhi Khan, Hassan Ali, Mohammed Fadel
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On the numerical solution of optimal control problems via Bell polynomials basis [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2020 We present a new numerical approach to solve the optimal control problems (OCPs) with a quadratic performance index. Our method is based on the Bell polynomials basis. The properties of Bell polynomials are explained.
M.R. Dadashi +3 more
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On Hermite-Hermite matrix polynomials [PDF]
Mathematica Bohemica, 2008 Summary: The definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented.
Metwally, M. S. +2 more
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Non-archimedean valuations of eigenvalues of matrix polynomials [PDF]
, 2016 We establish general weak majorization inequalities, relating the leading exponents of the eigenvalues of matrices or matrix polynomials over the field of Puiseux series with the tropical analogues of eigenvalues.
M. Akian, R. Bapat, S. Gaubert
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