Böttcher, Albrecht ; Grudsky, Sergei M. ; Maksimenko, Egor A. : On the structure of the eigenvectors of large Hermitian Toeplitz band matrices

Author(s):

Böttcher, Albrecht
Grudsky, Sergei M.
Maksimenko, Egor A.

Title:

On the structure of the eigenvectors of large Hermitian Toeplitz band matrices

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 5, 2009

Mathematics Subject Classification:

47B35			[ Toeplitz operators, Hankel operators, Wiener-Hopf operators ]
15A18			[ Eigenvalues, singular values, and eigenvectors ]
41A25			[ Rate of convergence, degree of approximation ]
65F15			[ Eigenvalues, eigenvectors ]

Abstract:

The paper is devoted to the asymptotic behavior of the eigenvectors of banded Hermitian Toeplitz matrices as the dimension of the matrices increases to infinity. The main result, which is based on certain assumptions, describes the structure of the eigenvectors in terms of the Laurent polynomial that generates the matrices up to an error term that decays exponentially fast. This result is applicable to both extreme and inner eigenvectors.

Keywords:

Toeplitz matrix, eigenvector, asymptotic expansions

Language:

English

Publication time:

2 / 2009