The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices. (English) Zbl 0788.65049
This paper studies the asymptotic spectra for Toeplitz or quasi-Toeplitz matrices of large order and small bandwidth. The analysis is split into one for the boundary condition independent and the dependent spectra, with algorithms for both. For such matrices of large order \((n\geq 100)\) that are nonnormal, the standard QR based eigenvalue algorithms will generally become useless unless a certain diagonal scaling is introduced that limits the growth of the associated eigenvectors. Various applications of finite difference approximations to partial differential equations are included.
Reviewer: F.Uhlig (Auburn)
MSC:
65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
15A18 | Eigenvalues, singular values, and eigenvectors |
65F35 | Numerical computation of matrix norms, conditioning, scaling |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |