Böttcher, Albrecht ; Grudsky, Sergei M. ; Maksimenko, Egor A. : On the structure of the eigenvectors of large Hermitian Toeplitz band matrices
Grudsky, Sergei M.
Maksimenko, Egor A.
- On the structure of the eigenvectors of large Hermitian Toeplitz band matrices
- Electronic source:
- Preprint series:
- Technische UniversitÃ¤t Chemnitz, FakultÃ¤t fÃ¼r 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 ]
- 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.
- Toeplitz matrix, eigenvector, asymptotic expansions
- Publication time:
- 2 / 2009