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The Solution of a Toeplitz Set of Linear Equations

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Published:01 April 1974Publication History
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Abstract

The solution of a set of m linear equations with a non-Hermitian Toeplitz associated matrix is considered. Presently available fast algorithms solve this set with 4m2 “operations” (an “operation” is defined here as a set of one addition and one multiplication). An improved algorithm requiring only 3m2 “operations” is presented.

References

  1. 1 ZOHAR, SHXLHAV. Toeplitz matrix inversion: The algorithm of W. F. Trench. J. ACM 16, 4 (Oct. 1969), 592-601. Google ScholarGoogle Scholar
  2. 2 LEVINSON, NORMAN. The Wiener RMS error criterion in filter design and prediction. J. Math. and Phys. 25, 4 (Jan. 1947), 261-278.Google ScholarGoogle Scholar
  3. 3 TRENCH, WILLIAM F. Weighting coefficients for the prediction of stationary time series from the finite past. SIAM J. Appl. Math. 15, 6 (Nov. 1967), 1502-1510.Google ScholarGoogle Scholar

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  1. The Solution of a Toeplitz Set of Linear Equations

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        cover image Journal of the ACM
        Journal of the ACM  Volume 21, Issue 2
        April 1974
        176 pages
        ISSN:0004-5411
        EISSN:1557-735X
        DOI:10.1145/321812
        Issue’s Table of Contents

        Copyright © 1974 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 April 1974
        Published in jacm Volume 21, Issue 2

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