Numerical validation method for nonlinear equations using interval analysis and rational arithmetic

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    Abstract

    This paper proposes an algorithm with a guaranteed accuracy for the finite-dimensional nonlinear equation. First, an algorithm is shown which can determine the interval containing the true solution, based on the given approximate solution. The method is based on the interval analysis and considers the representation error of the equation. Then the interval iteration method is shown which can arbitrarily reduce the interval. The rational number arithmetic is used and the rounding of the rational number is utilized effectively. Finally, an experimental implementation of the algorithm on a computer is presented, together with some numerical examples.

    Original languageEnglish
    Pages (from-to)99-112
    Number of pages14
    JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
    Volume78
    Issue number7
    Publication statusPublished - 1995 Jul

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    Nonlinear equations
    Numerical methods

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering

    Cite this

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    abstract = "This paper proposes an algorithm with a guaranteed accuracy for the finite-dimensional nonlinear equation. First, an algorithm is shown which can determine the interval containing the true solution, based on the given approximate solution. The method is based on the interval analysis and considers the representation error of the equation. Then the interval iteration method is shown which can arbitrarily reduce the interval. The rational number arithmetic is used and the rounding of the rational number is utilized effectively. Finally, an experimental implementation of the algorithm on a computer is presented, together with some numerical examples.",
    author = "Masahide Kashiwagi and Shinichi Oishi",
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