Tridiagonal Approach to the Algebraic Environment of Toeplitz Matrices, Part I: Basic Results

DOI10.1137/0612018zbMath0728.65020OpenAlexW2052378309MaRDI QIDQ3352367

Y. Genin, Philippe Delsarte

Publication date: 1991

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0612018

zbMATH Keywords

three-term recurrence relationlinear prediction problemtridiagonal reductionsplit Levinson algorithmnonnegative- definite Hermitian Toeplitz matricessymmetric predictor polynomialsToeplitz algorithm

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Direct numerical methods for linear systems and matrix inversion (65F05) Prediction theory (aspects of stochastic processes) (60G25) Probabilistic methods, stochastic differential equations (65C99)

Related Items (18)

Markov's theorem for weight functions on the unit circle ⋮ Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle ⋮ A note on Wall's modification of the Schur algorithm and linear pencils of Jacobi matrices ⋮ Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators ⋮ CMV matrices and little and big \(-1\) Jacobi polynomials ⋮ Monotonicity of zeros for a class of polynomials including hypergeometric polynomials ⋮ SzegÖ polynomials on the real axis ⋮ On monotonicity of zeros of paraorthogonal polynomials on the unit circle ⋮ A CMV connection between orthogonal polynomials on the unit circle and the real line ⋮ On an inverse eigenvalue problem for unitary Hessenberg matrices ⋮ Perturbation and interlace theorems for the unitary eigenvalue problem ⋮ On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval ⋮ Orthogonal polynomials and quadrature rules on the unit circle associated with perturbations of symmetric measures ⋮ Zeros of quasi-paraorthogonal polynomials and positive quadrature ⋮ Elliptic polynomials orthogonal on the unit circle with a dense point spectrum ⋮ Inverse eigenvalue problem of unitary Hessenberg matrices ⋮ Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle ⋮ Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circle

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