The paper deals with the entries of functions of large banded Hermitian block Toeplitz matrices and their perturbations. For general continuous functions, convergence results are established, and for analytic functions, these results are accompanied by estimates of the convergence speed. The applica
On the Elementwise Convergence of Continuous Functions of Hermitian Banded Toeplitz Matrices
✍ Scribed by Pedro M. Crespo; Jess Gutierrez-Gutierrez
- Book ID
- 114640623
- Publisher
- IEEE
- Year
- 2007
- Tongue
- English
- Weight
- 466 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0018-9448
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📜 SIMILAR VOLUMES
We are concerned with the behavior of the minimum (maximum) eigenvalue A~0 "~ (A~ "~) of an (n + 1) X (n + 1) Hermitian Toeplitz matrix T~(f) where f is an integrable real-valued function. Kac, Murdoch, and Szeg5, Widom, Patter, and R. H. Chan obtained that A}~ 0 -rain f = O(1/n 2k) in the case whe
## Abstract Let __λ__ be an eigenvalue of an infinite Toeplitz band matrix __A__ and let __λ~n~__ be an eigenvalue of the __n__ ×__n__ truncation __A~n~__ of __A__ . Suppose __λ~n~__ converges to __λ__ as __n__ → ∞. We show that generically the eigenspaces for __λ~n~__ are onedimensional and contai