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research-article

Seeking better algorithms for approximate GCD

Published: 18 May 2017 Publication History

Abstract

We are interested in seeking better algorithms by just slightly updating and combining the well-known algorithms for the following well-known problem in Symbolic-Numeric Computations.

References

[1]
D. A. Bini and P. Boito. Structured matrix-based methods for polynomial ϵ-gcd: Analysis and comparisons. In Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, ISSAC '07, pages 9--16, New York, NY, USA, 2007. ACM.
[2]
P. Boito. Structured Matrix Based Methods for Approximate GCD. Ph.D. Thesis. Department of Mathematics, University of Pisa, Italia, 2007.
[3]
R. M. Corless, S. M. Watt, and L. Zhi. QR factoring to compute the GCD of univariate approximate polynomials. IEEE Trans. Signal Process., 52(12):3394--3402, 2004.
[4]
K. Nagasaka and T. Masui. Extended qrgcd algorithm. In Proceedings of the 15th International Workshop on Computer Algebra in Scientific Computing - Volume 8136, CASC 2013, pages 257--272, New York, NY, USA, 2013. Springer-Verlag New York, Inc.
[5]
Z. Zeng. The numerical greatest common divisor of univariate polynomials. In Randomization, relaxation, and complexity in polynomial equation solving, volume 556 of Contemp. Math., pages 187--217. Amer. Math. Soc., Providence, RI, 2011.

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    Published In

    cover image ACM Communications in Computer Algebra
    ACM Communications in Computer Algebra  Volume 51, Issue 1
    March 2017
    37 pages
    ISSN:1932-2232
    EISSN:1932-2240
    DOI:10.1145/3096730
    Issue’s Table of Contents

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 18 May 2017
    Published in SIGSAM-CCA Volume 51, Issue 1

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