Approximating Inverse of Toeplitz Matrices by Circulant Matrices
Bottcher, A. ; Grudsky, S. M. ; Ramirez de Arellano, E.
Methods Appl. Anal., Tome 11 (2004) no. 1, p. 211-220 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2004-06-14
Classification:  
@article{1119019654,
     author = {Bottcher, A. and Grudsky, S. M. and Ramirez de Arellano, E.},
     title = {Approximating Inverse of Toeplitz Matrices by Circulant Matrices},
     journal = {Methods Appl. Anal.},
     volume = {11},
     number = {1},
     year = {2004},
     pages = { 211-220},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1119019654}
}

Bottcher, A.; Grudsky, S. M.; Ramirez de Arellano, E. Approximating Inverse of Toeplitz Matrices by Circulant Matrices. Methods Appl. Anal., Tome 11 (2004) no. 1, pp.  211-220. http://gdmltest.u-ga.fr/item/1119019654/