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Asymptotic eigenvalue distribution of block-Toeplitz matrices

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2 Author(s)
N. K. Bose ; Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA, USA ; K. J. Boo

The need for approximating block-Toeplitz with Toeplitz block matrices by means of block-circulant with circulant block matrices with the objective of transforming an inherently ill-posed image deconvolution problem to a well-posed one motivated a surge of papers on the analysis of the quality as well as the speed of convergence of the algorithms that produce such approximants to serve as preconditioners for conjugate-gradient methods. This correspondence contributes to that surge by giving a simple proof of the fact that the sequence of eigenvalues of the Hermitian block Toeplitz with Toeplitz-block matrices are asymptotically equidistributed. To do this, Weyl's (1916) results on the distribution properties of multidimensional sequences are exploited. Inferences to related results are made

Published in:

IEEE Transactions on Information Theory  (Volume:44 ,  Issue: 2 )