An L-Banded Approximation to the Inverse of Symmetric Toeplitz Matrices

Benassi Romain, Pievatolo Antonio and Göb Rainer
Additional contact information
Benassi Romain: Telecom Bretagne, France. E-mail: romain.benassi@telecom-bretagne.eu
Pievatolo Antonio: CNR IMATI, Via Bassini 15, 20133 Milano, Italy. E-mail: antonio.pievatolo@mi.imati.cnr.it
Göb Rainer: Würzburg University, Germany. E-mail: goeb@mathematik.uni-wuerzburg.de

Stochastics and Quality Control, 2010, vol. 25, issue 1, 13-30

Abstract: We apply the banded matrix inversion theorem given by Kavcic and Moura [IEEE Trans. Inf. Theory 46: 1495–1509, 2000] to symmetric Toeplitz matrices. If the inverse is banded with bandwidth smaller than its size, there is a gain in arithmetic complexity compared to the current methods for Toeplitz matrix inversion. Our algorithm can also be used to find an approximation of the inverse matrix even though it is not exactly banded, but only well localized around its diagonal.

Keywords: Symmetric Toeplitz matrix; trench matrix; matrix inversion; banded matrix; correlation matrix (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1515/eqc.2010.002

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