research-article

A fast iterative algorithm for the large-scale toeplitz linear systems

Authors:

Shuichi Yasumura,

Lei LiAuthors Info & Claims

RACS '15: Proceedings of the 2015 Conference on research in adaptive and convergent systems

Pages 27 - 31

https://doi.org/10.1145/2811411.2811489

Published: 09 October 2015 Publication History

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Abstract

This paper proposes a fast iterative algorithm for solving the large-scale Toeplitz linear systems. This method used the fast O(n log2 n) direct algorithm for solving a triangular Toeplitz linear systems which is shown in [1], and introduces the (I+S) type precondition Gauss-Seidel iteration to apply to a general large-scale Toeplitz linear systems. The new method combined the good point in both the fast direct algorithm and precondition iterative method. Some numerical experiments showed the proposed method can get the best or the better evaluation for the computational time cost by comparison with Levinson's algorithm (direct method), PCG algorithm (iterative method) and BiCG algorithm (iterative method).

References

[1]

Zhaoyong You and Lei Li, 1987, The Time Complexity of Triangular Toeplitz Systems, Mathematica Numerica Sinica, vol.9, no.3, pp. 282--285.

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[2]

G. Codevico, G. Heinig, and M. Van Barel, 2004, A Superfast Solver for Real Symmetric Toeplitz Systems using Real Trigonometric Transformations, Department of Computer Science, K. U. Leuven, Report TW 386, Leuven, Belgium, February, 2004.

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[3]

N. Levinson, 1947, The Wiener RMS Error Criterion in Filter Design and Prediction. J. Mathematical Phys., vol. 25, pp. 261--278.

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[4]

M. Porsani and T. J. Ulrych, 1991, Levinson-Type Extensions for Non-Toeplitz Systems, IEEE Trans. on Signal Processing, vol. 39, no.2, pp. 366--375.

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[5]

A. D. Gunawardena, S. K. Jain and L. Snyder, 1991, Modified Iterative Methods for Consistent Linear Systems, Linear Algebra Appl. vol.154--156, pp.123--143.

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Index Terms

A fast iterative algorithm for the large-scale toeplitz linear systems
1. Theory of computation
  1. Logic
    1. Linear logic

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Published In

RACS '15: Proceedings of the 2015 Conference on research in adaptive and convergent systems

October 2015

540 pages

ISBN:9781450337380

DOI:10.1145/2811411

Conference Chairs:
Esmaeil S. Nadimi
University of Southern Denmark, Denmark
,
Tomas Cerny
Czech Technical University, Czech Republic
,
Program Chairs:
Sung-Ryul Kim
Konkuk University, Korea
,
Wei Wang
San Diego State University

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Association for Computing Machinery

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Published: 09 October 2015

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RACS '15: International Conference on Research in Adaptive and Convergent Systems

October 9 - 12, 2015

Prague, Czech Republic

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RACS '15 Paper Acceptance Rate 75 of 309 submissions, 24%;

Overall Acceptance Rate 393 of 1,581 submissions, 25%

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A fast algorithm for solving diagonally dominant symmetric pentadiagonal Toeplitz systems

A communication-less parallel algorithm for tridiagonal Toeplitz systems

Erratum to: "On the HSS iteration methods for positive definite Toeplitz linear systems" [J. Comput. Appl. Math. 224 (2009) 709-718]

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