Asymptotics of Eigenvectors of Large Symmetric Banded Toeplitz Matrices

作者：Batalshchikov A^*; Grudsky S; Ramirez de Arellano E; Stukopin V

来源：Integral Equations and Operator Theory, 2015, 83(3): 301-330.

DOI：10.1007/s00020-015-2257-y

• Toeplitz matrices
• Eigenvectors
• Asymptotic expansions

The paper studies the asymptotic behavior of all eigenvectors of banded symmetric (in general non-Hermitian) Toeplitz matrices as the dimension of the matrices tends to infinity. The main result describes, given certain assumptions, the structure of the eigenvectors in terms of the Laurent polynomial which generates the matrices, up to an error term that decays exponentially. The effectiveness of the formulas is confirmed by some numerical examples.

• 出版日期2015-11