Title :
Asymptotic eigenvalue distribution of block-Toeplitz matrices
Author :
Bose, N.K. ; Boo, K.J.
Author_Institution :
Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA, USA
fDate :
3/1/1998 12:00:00 AM
Abstract :
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
Keywords :
Hermitian matrices; Toeplitz matrices; approximation theory; conjugate gradient methods; convergence of numerical methods; deconvolution; eigenvalues and eigenfunctions; image sequences; Hermitian block Toeplitz matrices; Toeplitz block matrices; approximants; asymptotic eigenvalue distribution; block-Toeplitz matrices; block-circulant matrices; circulant block matrices; conjugate-gradient method; convergence; distribution properties; ill-posed image deconvolution problem; images; multidimensional sequences; preconditioners; well-posed problem; Algorithm design and analysis; Convergence; Deconvolution; Eigenvalues and eigenfunctions; Image analysis; Image restoration; Least squares approximation; Multidimensional systems; Surges; Transmission line matrix methods;
Journal_Title :
Information Theory, IEEE Transactions on
