Orthogonal matrix polynomials and applications

DOI10.1016/0377-0427(95)00193-XzbMath0863.42018MaRDI QIDQ1919056

Walter Van Assche, Ann Sinap

Publication date: 13 October 1996

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Gaussian quadratureorthogonal matrix polynomialsblock tridiagonal matricesblock Hessenberg matricesmultichannel time series

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Numerical quadrature and cubature formulas (65D32)

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Cites Work

• Unnamed Item
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• Applications of Szegö polynomials to digital signal processing
• A divide and conquer method for unitary and orthogonal eigenproblems
• Discrete Sturm-Liouville operators and some problems of function theory
• Asymptotics for zeros of Szegő polynomials associated with trigonometric polynomial signals
• Divide and conquer algorithms for the bandsymmetric eigenvalue problem
• On a class of matrix orthogonal polynomials on the real line
• Orthogonal matrix-valued polynomials and applications. Seminar on operator theory at the School of Mathematical Sciences, Tel Aviv University (1987-1988)
• Polynomial interpolation and Gaussian quadrature for matrix-valued functions
• Asymptotics for Szegö polynomials associated with Wiener-Levinson filters
• Szegő polynomials applied to frequency analysis
• A class of matrix orthogonal polynomials on the unit circle
• Scattering theory and matrix orthogonal polynomials on the real line
• Orthogonal matrix polynomials and higher-order recurrence relations
• Weak convergence of orthogonal polynomials
• Gaussian quadrature for matrix valued functions on the real line
• Gaussian quadrature for matrix valued functions on the unit circle
• Szegö polynomials associated with Wiener-Levinson filters
• On the distribution of zeros of polynomials orthogonal on the unit circle
• Bauer-type factorization of positive matrices and the theory of matrix polynomials orthogonal on the unit circle
• Matrix Analysis
• Inverses of Toeplitz Operators, Innovations, and Orthogonal Polynomials
• Orthogonal polynomial matrices on the unit circle
• An implementation of a divide and conquer algorithm for the unitary eigen problem
• Matrix orthogonal polynomials on the unit circle