An eigenvalue localization theorem for pentadiagonal symmetric Toeplitz matrices

DOI10.1016/j.laa.2011.05.025zbMath1230.15017OpenAlexW1977691736MaRDI QIDQ636263

Mohamed Elouafi

Publication date: 26 August 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.05.025

zbMATH Keywords

eigenvaluedeterminantNewton methodsChebyshev polynomialeigenvalue boundsbisectional methodspentadiagonal symmetric Toeplitz matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenvalues, singular values, and eigenvectors (15A18) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (14)

On formulae for the determinant of symmetric pentadiagonal Toeplitz matrices ⋮ On the spectrum of banded Hankel matrices ⋮ Explicit inversion of Band Toeplitz matrices by discrete Fourier transform ⋮ Distribution of eigenvalues for sub-skewtriagonal Hankel matrices ⋮ A linear algebra approach to HP-splines frequency parameter selection ⋮ On computing the eigenvalues of band Toeplitz matrices ⋮ Finding eigenvalues for heptadiagonal symmetric Toeplitz matrices ⋮ Unnamed Item ⋮ A Widom like formula for some Toeplitz plus Hankel determinants ⋮ On a relationship between Chebyshev polynomials and Toeplitz determinants ⋮ On a homogeneous recurrence relation for the determinants of general pentadiagonal Toeplitz matrices ⋮ A reducing approach for symmetrically sparse banded and anti-banded matrices ⋮ Numerical range of a nilpotent matrix and related central force ⋮ Some determinantal considerations for pentadiagonal matrices

Cites Work

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• Inside the eigenvalues of certain Hermitian Toeplitz band matrices
• Spectral and structural properties of some pentadiagonal symmetric matrices
• On the inverse problem of constructing symmetric pentadiagonal Toeplitz matrices from their three largest eigenvalues
• An Algorithm for the Inversion of Finite Toeplitz Matrices
• Spectral Properties of Banded Toeplitz Matrices

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