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Orthogonal Matrix Laurent Polynomials
Mathematical Notes, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Modified Moments and Matrix Orthogonal Polynomials
Acta Applicandae Mathematica, 2000It is known that, in the scalar case, a good via to compute recurrence coefficients of polynomials orthogonal with respect to a nonnegative measure is the modified Chebyshev algorithm [cf. \textit{R. A. Sack} and \textit{A. F. Donavan}, Numer. Math. 18, 465-478 (1972; Zbl 0221.65041)]. This algorithm, recently extended to the vector case [cf.
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Markov's Theorem for Orthogonal Matrix Polynomials
Canadian Journal of Mathematics, 1996AbstractMarkov's Theorem shows asymptotic behavior of the ratio between the n-th orthonormal polynomial with respect to a positive measure and the n-th polynomial of the second kind. In this paper we extend Markov's Theorem for orthogonal matrix polynomials.
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1990
An overview is given of some classical and recent results concerning zeros of orthogonal matrix polynomials on the unit circle. The basic questions are: How these zeros are located in the complex plane? Conversely, what conditions on the location of the zeros of a given matrix polynomial ensure that the polynomial is orthogonal?
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An overview is given of some classical and recent results concerning zeros of orthogonal matrix polynomials on the unit circle. The basic questions are: How these zeros are located in the complex plane? Conversely, what conditions on the location of the zeros of a given matrix polynomial ensure that the polynomial is orthogonal?
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Skew-orthogonal polynomials and random-matrix ensembles
Physical Review E, 2002There is considerable interest in understanding the relation between random-matrix ensembles and quantum chaotic systems in the context of the universality of energy-level correlations. In this connection, while Gaussian ensembles of random matrices have been studied extensively, not much is known about ensembles with non-Gaussian weight functions ...
Ghosh, Saugata, Pandey, Akhilesh
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Quadratic decomposition of orthogonal polynomials: a matrix approach
Numerical Algorithms, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francisco Marcellán, Gabriela Sansigre
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Rectangular matrix Padé approximants and square matrix orthogonal polynomials
Numerical Algorithms, 1997Using the method of linear functionals introduced by \textit{C. Brezinski} [Padé-type approximation and general orthogonal polynomials (1980; Zbl 0418.41012] the authors study rectangular (left) matrix Padé approximants to formal power series with \(p\times q\) matrices as coefficients. The parallel to the classical scalar case is remarkable. Existence
André Draux, Borhane Moalla
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Discrete orthogonal matrix polynomials
Analysis Mathematica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Matrix factorizations and orthogonal polynomials
Random Matrices: Theory and Applications, 2019We present some elements of the theory of orthogonal polynomials based on matrix decompositions. We focus our attention on discrete linear functionals, and use the Meixner polynomials as a concrete example.
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Matrix transformations of series of orthogonal polynomials
Mathematika, 1995For a sequence of polynomials \((P_n)\) orthonormal on the interval \([- 1, 1]\), the sequence of transforms \((g_n)\) of the series \(\sum^\infty_{k= 0} a_k P_k(u)\) given by \(g_n(u):= \sum^\infty_{k= 0} b_{nk} a_k P_k(u)\) is considered. Necessary and sufficient conditions on the the matrix \((b_{nk})\) are established for the sequence \((g_n)\) to ...
Borwein, David +2 more
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