On a relationship between Chebyshev polynomials and Toeplitz determinants

DOI10.1016/j.amc.2013.12.029zbMath1364.15022OpenAlexW2017529143MaRDI QIDQ530001

Mohamed Elouafi

Publication date: 9 June 2017

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

Full work available at URL: https://doi.org/10.1016/j.amc.2013.12.029

zbMATH Keywords

Chebyshev polynomialsToeplitz determinantsBaxter and Schmidt formula

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Toeplitz, Cauchy, and related matrices (15B05)

Related Items

On formulae for the determinant of symmetric pentadiagonal Toeplitz matrices ⋮ Relationships between the permanents of a certain type of \(k\)-tridiagonal symmetric Toeplitz matrix and the Chebyshev polynomials ⋮ Symmetric polynomials in the symplectic alphabet and the change of variables \(z_j = x_j + x_j^{-1}\) ⋮ On One Type of Generalized Vandermonde Determinants ⋮ Explicit inversion of Band Toeplitz matrices by discrete Fourier transform ⋮ Distribution of eigenvalues for sub-skewtriagonal Hankel matrices ⋮ A cost-efficient numerical algorithm for the determinants of heptadiagonal matrices with Toeplitz structure ⋮ Recurrence form for determinant of a heptadiagonal symmetric Toeplitz matrix ⋮ A Widom like formula for some Toeplitz plus Hankel determinants ⋮ Sextic reciprocal monogenic dihedral polynomials ⋮ Infinite families of reciprocal monogenic polynomials and their Galois groups ⋮ Exact equivalences and phase discrepancies between random matrix ensembles

Cites Work

• Unnamed Item
• An eigenvalue localization theorem for pentadiagonal symmetric Toeplitz matrices
• Determinants and their applications in mathematical physics
• Finding eigenvalues for heptadiagonal symmetric Toeplitz matrices
• Spectral Properties of Banded Toeplitz Matrices
• Determinants of a Certain Class of Non-Hermitian Toeplitz Matrices.