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On the condition numbers of large semidefinite Toeplitz matrices

✍ Scribed by Albrecht Böttcher; Sergei M. Grudsky

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
915 KB
Volume
279
Category
Article
ISSN
0024-3795

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✦ Synopsis

This Paper is devoted to asymptotic estimates for the (spectral or Euclidean) condition numbers K(T'(u)) = l~T,(a)IlllT;'(a)/l f 1, g o dr e n x n Toeplitz matrices TH(u) in the case where the Symbol a is an L" function and Re a 3 0 almost everywhere. We describe several classes of Symbols a for which K(T~(~))

increases like (log n)', n', or even e"".

📜 SIMILAR VOLUMES

On the asymptotic behavior of the eigenv
On the asymptotic behavior of the eigenvectors of large banded Toeplitz matrices
✍ A. Böttcher; S. Grudsky; E. Ramírez de Arellano 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB 👁 1 views

## 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