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Towards Industrial Application of Approximate Computer Algebra

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Book cover Computer Algebra in Scientific Computing (CASC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8136))

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Abstract

The approximate computer algebra has scarcely been used for computations in industry so far. In order to break through this situation, we consider the series expansion of multivariate eigenvalues at their critical points in an aircraft control model. We show that the approximate square-free decomposition of univariate polynomial is quite useful in finding critical points semi-numerically and that the approximate factorization is successfully used for factoring multivariate polynomials with floating-point number coefficients. Furthermore, the “effective floating-point numbers” are quite useful in eliminating fully-erroneous terms from small but meaningful terms.

Work supported by Japan Society for the Promotion of Science under Grants 23500003.

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Author information

Authors and Affiliations

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

    Tateaki Sasaki

  2. Japanese Association of Mathematics Certification, Ueno 5-1-1, Tokyo, 110-0005, Japan

    Daiju Inaba

  3. Dept. Info. Comp. Sci., Nara Women’s University, Nara-city, Nara, 630-8506, Japan

    Fujio Kako

Authors
  1. Tateaki Sasaki
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  2. Daiju Inaba
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  3. Fujio Kako
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

  4. Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2013 Springer International Publishing Switzerland

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Sasaki, T., Inaba, D., Kako, F. (2013). Towards Industrial Application of Approximate Computer Algebra. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_26

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  • DOI: https://doi.org/10.1007/978-3-319-02297-0_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02296-3

  • Online ISBN: 978-3-319-02297-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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