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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Benassi Romain & Pievatolo Antonio & Göb Rainer, 2010. "An L-Banded Approximation to the Inverse of Symmetric Toeplitz Matrices," Stochastics and Quality Control, De Gruyter, vol. 25(1), pages 13-30, January.
    • Handle: RePEc:bpj:ecqcon:v:25:y:2010:i:1:p:13-30:n:3
    DOI: 10.1515/eqc.2010.002
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    References listed on IDEAS

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    1. Pascal Bondon, 2001. "Recursive Relations for Multistep Prediction of a Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 399-410, July.
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