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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:
Information Theory, IEEE Transactions on
(Volume:44
,
Issue:
2
)
Date of Publication: Mar 1998
- Page(s):
- 858 - 861
- ISSN :
- 0018-9448
- INSPEC Accession Number:
- 5873599
- Digital Object Identifier :
- 10.1109/18.661535
- Product Type:
- Journals & Magazines
- Date of Current Version :
- 06 August 2002
- Issue Date :
- Mar 1998
- Sponsored by :
- IEEE Information Theory Society
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