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Toeplitz Matrix Inversion: The Algorithm of W. F. Trench
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Source Journal of the ACM (JACM) archive
Volume 16 ,  Issue 4  (October 1969) table of contents
Pages: 592 - 601  
Year of Publication: 1969
ISSN:0004-5411
Author
Shalhav Zohar  Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 23,   Downloads (12 Months): 241,   Citation Count: 6
Additional Information:

abstract   references   cited by   index terms  

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ABSTRACT

The algorithm of W. F. Trench for the inversion of Toeplitz matrices is presented with a detailed proof for the case of non-Hermitian matrices. The only condition necessary to insure the validity of the algorithm is that all principal minors be nonzero.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
TRENCH, W.F. An algorithm for the inversion of finite Toeplitz matrices. J. SIAM 12, 3 (Sept. 1964), 515-522.

CITED BY  6
David C. Farden, The Solution of a Special Set of Hermitian Toeplitz Linear Equations, ACM Transactions on Mathematical Software (TOMS), v.3 n.2, p.159-163, June 1977
Shalhav Zohar, The Solution of a Toeplitz Set of Linear Equations, Journal of the ACM (JACM), v.21 n.2, p.272-276, April 1974
G. A. Watson, An Algorithm for the Inversion of Block Matrices of Toeplitz Form, Journal of the ACM (JACM), v.20 n.3, p.409-415, July 1973
Ellis Horowitz, The application of symbolic mathematics to a singular perturbation problem, Proceedings of the ACM annual conference, p.816-825, August 01-01, 1972, Boston, Massachusetts, United States
Nancy M. Huang , Randall E. Cline, Inversion of Persymmetric Matrices Having Toeplitz Inverses, Journal of the ACM (JACM), v.19 n.3, p.437-444, July 1972
Abdulla Firag , Lee M. Garth, Adaptive joint decoding and equalization for space-time block-coded amplify-and-forward relaying systems, IEEE Transactions on Signal Processing, v.57 n.3, p.1163-1176, March 2009

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Matrix inversion

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices


General Terms:
Algorithms, Performance, Theory


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