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June 2004 Approximating Inverse of Toeplitz Matrices by Circulant Matrices
A. Bottcher, S. M. Grudsky, E. Ramirez de Arellano
Methods Appl. Anal. 11(2): 211-220 (June 2004).


With every continuous function a on the complex unit circle one can associate a sequence {Tn(a)}infinity n=1 of Toeplitz matrices and a sequence {Cn(a)} infinityn=1 of circulant matrices. By employing some advanced results on the finite sections of Toeplitz operators, we prove asymptotic estimates for the central columns of the matrices Tn-1(a) - Cn -1(a)as n goes to infinity. Our results generalize and sharpen recent results by T. Strohmer and by F.-W. Sun, Y. Jiang, and J. S. Baras, who also discussed the relevancy of the problem in signal processing.


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A. Bottcher. S. M. Grudsky. E. Ramirez de Arellano. "Approximating Inverse of Toeplitz Matrices by Circulant Matrices." Methods Appl. Anal. 11 (2) 211 - 220, June 2004.


Published: June 2004
First available in Project Euclid: 17 June 2005

zbMATH: 1097.47028
MathSciNet: MR2143520

Rights: Copyright © 2004 International Press of Boston


Vol.11 • No. 2 • June 2004
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