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International Workshop on Computer Algebra in Scientific Computing

CASC 2010: Computer Algebra in Scientific Computing pp 220–231Cite as

Term Cancellations in Computing Floating-Point Gröbner Bases

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6244))

Abstract

We discuss the term cancellation which makes the floating-point Gröbner basis computation unstable, and show that error accumulation is never negligible in our previous method. Then, we present a new method, which removes accumulated errors as far as possible by reducing matrices constructed from coefficient vectors by the Gaussian elimination. The method manifests amounts of term cancellations caused by the existence of approximate linearly dependent relations among input polynomials.

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Author information

Authors and Affiliations

  1. Professor emeritus, University of Tsukuba, Tsukuba-city, Ibaraki, 305-8571, Japan

    Tateaki Sasaki

  2. Department of Info. and Comp. Sci., Nara Women’s University, Nara-city, 630-8506, Japan

    Fujio Kako

Authors
  1. Tateaki Sasaki
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  2. Fujio Kako
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Editor information

Editors and Affiliations

  1. JINR, Moscow region, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. University of Kassel, 34109 l, Kasse, Germany

    Wolfram Koepf

  3. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

  4. Russian Academy of Sciences,, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Sasaki, T., Kako, F. (2010). Term Cancellations in Computing Floating-Point Gröbner Bases. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2010. Lecture Notes in Computer Science, vol 6244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15274-0_20

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  • DOI: https://doi.org/10.1007/978-3-642-15274-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15273-3

  • Online ISBN: 978-3-642-15274-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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