Five-Diagonal Toeplitz Determinants an Their Relation to Chebyshev Polynomials

DOI10.1137/0609048zbMath0661.15006OpenAlexW2019701372MaRDI QIDQ3809925

George Hoagland Vineyard, Robert B. Marr

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1137/0609048

zbMATH Keywords

Chebyshev polynomialsgenerating functionfive-diagonal Toeplitz determinants

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (16)

On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle ⋮ Maximum of the resolvent over matrices with given spectrum ⋮ An efficient numerical algorithm for the determinant of a cyclic pentadiagonal Toeplitz matrix ⋮ The use of the factorization of five-diagonal matrices by tridiagonal Toeplitz matrices ⋮ Sequences of numbers meet the generalized Gegenbauer-Humbert polynomials ⋮ A tridiagonalization-based numerical algorithm for computing the inverses of \((p, q)\)-pentadiagonal matrices ⋮ An explicit formula for the smoother weights of the Hodrick-Prescott filter ⋮ An explicit formula for the inverse of a pentadiagonal Toeplitz matrix ⋮ Eigenpairs of some imperfect pentadiagonal Toeplitz matrices ⋮ Explicit inverse of near Toeplitz pentadiagonal matrices related to higher order difference operators ⋮ On a homogeneous recurrence relation for the determinants of general pentadiagonal Toeplitz matrices ⋮ Sequences of non-Gegenbauer-Humbert polynomials meet the generalized Gegenbauer-Humbert polynomials ⋮ On determinants of cyclic pentadiagonal matrices with Toeplitz structure ⋮ The determinants of certain \((0,1)\) Toeplitz matrices ⋮ Some determinantal considerations for pentadiagonal matrices ⋮ Determinants of some pentadiagonal matrices

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