A. Böttcher; S. M. Grudsky : Estimates for the condition numbers of large semi-definite Toeplitz matrices
- Author(s) :
- A. Böttcher; S. M. Grudsky
- Title :
- Estimates for the condition numbers of large semi-definite Toeplitz matrices
- Electronic source :
- [gzipped dvi-file] 54
kB
[gzipped ps-file] 136 kB
- Preprint series
- Technische Universität Chemnitz-Zwickau, Fakultät für Mathematik (Germany). Preprint 97-13, 1997
- Mathematics Subject Classification :
- 47B35 [ Toeplitz operators, etc.
]
- Abstract :
- This paper is devoted to asymptotic estimates for the condition numbers
$\kappa(T_n(a))=||T_n(a)|| ||T_n^(-1)(a)||$
of large $n\cross n$ Toeplitz matrices $T_N(a)$ in the case where $\alpha \element L^\infinity$ and $Re \alpha \ge 0$ . We describe several classes of symbols $\alpha$ for which $\kappa(T_n(a))$ increases like $(log n)^\alpha, n^\alpha$ , or even $e^(\alpha n)$ . The consequences of the results for singular values, eigenvalues, and the finite section method are discussed. We also consider Wiener-Hopf integral operators and multidimensional Toeplitz operators.
- Keywords :
- Toeplitz operator, Toeplitz matrices, singular values, eigenvalues, Wiener-Hopf
- Language :
- english
- Publication time :
- 5/1997
