Finding all solutions of nonlinear systems of equations using linear programming with guaranteed accuracy

Yusuke Nakaya, Shinichi Oishi

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    A linear programming-based method is presented for finding all solutions of nonlinear systems of equations with guaranteed accuracy. In this method, a new effective linear programming-based method is used to delete regions in which solutions do not exist. On the other hand, Krawczyk's method is used to find regions in which solutions exist. As an illustrative example, all solutions of the nonlinear system of equations describing equilibrium conditions of the "high polymer liquid system", which is a well-known ill-conditioned system of equations, are identified by the method.

    Original languageEnglish
    Pages (from-to)171-177
    Number of pages7
    JournalJournal of Universal Computer Science
    Volume4
    Issue number2
    Publication statusPublished - 1998

    Fingerprint

    Nonlinear Systems of Equations
    Linear programming
    Nonlinear systems
    Liquids
    Polymers
    System of equations
    Liquid

    Keywords

    • All Solutions
    • Guaranteed Accuracy
    • Krawczyk's Method
    • Linear Programming
    • Nonlinear Equations

    ASJC Scopus subject areas

    • Computer Science(all)

    Cite this

    Finding all solutions of nonlinear systems of equations using linear programming with guaranteed accuracy. / Nakaya, Yusuke; Oishi, Shinichi.

    In: Journal of Universal Computer Science, Vol. 4, No. 2, 1998, p. 171-177.

    Research output: Contribution to journalArticle

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