A method which finds the maxima and minima of a multivariable function applying affine arithmetic

Shinya Miyajima, Masahide Kashiwagi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A new method is proposed for finding all maxima and minima of a multivariable function f in a box X (0). In this method, the maxima and the minima are calculated by dividing X (0) into subrogions recursively and bounding the ranges of f in the each subregion applying affine arithmetic and discarding the subrogions which don't possess the possibility of including the point that the maximum (minimum) value occurs. Moreover, to discard more subrogions in initial stage, i.e. to speed the new method, two algorithms are introduced. And to show the efficiency of the new method, some numerical examples are implemented.

    Original languageEnglish
    Title of host publicationLecture Notes in Computer Science
    EditorsZ. Li, L. Vulkov, J. Wasniewski
    Pages424-431
    Number of pages8
    Volume3401
    Publication statusPublished - 2005
    EventThird International Conference on Numerical Analysis and Its Applications, NAA 2004 - Rousse, Bulgaria
    Duration: 2004 Jun 292004 Jul 3

    Other

    OtherThird International Conference on Numerical Analysis and Its Applications, NAA 2004
    CountryBulgaria
    CityRousse
    Period04/6/2904/7/3

    Fingerprint

    Numerical methods

    ASJC Scopus subject areas

    • Computer Science (miscellaneous)

    Cite this

    Miyajima, S., & Kashiwagi, M. (2005). A method which finds the maxima and minima of a multivariable function applying affine arithmetic. In Z. Li, L. Vulkov, & J. Wasniewski (Eds.), Lecture Notes in Computer Science (Vol. 3401, pp. 424-431)

    A method which finds the maxima and minima of a multivariable function applying affine arithmetic. / Miyajima, Shinya; Kashiwagi, Masahide.

    Lecture Notes in Computer Science. ed. / Z. Li; L. Vulkov; J. Wasniewski. Vol. 3401 2005. p. 424-431.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Miyajima, S & Kashiwagi, M 2005, A method which finds the maxima and minima of a multivariable function applying affine arithmetic. in Z Li, L Vulkov & J Wasniewski (eds), Lecture Notes in Computer Science. vol. 3401, pp. 424-431, Third International Conference on Numerical Analysis and Its Applications, NAA 2004, Rousse, Bulgaria, 04/6/29.
    Miyajima S, Kashiwagi M. A method which finds the maxima and minima of a multivariable function applying affine arithmetic. In Li Z, Vulkov L, Wasniewski J, editors, Lecture Notes in Computer Science. Vol. 3401. 2005. p. 424-431
    Miyajima, Shinya ; Kashiwagi, Masahide. / A method which finds the maxima and minima of a multivariable function applying affine arithmetic. Lecture Notes in Computer Science. editor / Z. Li ; L. Vulkov ; J. Wasniewski. Vol. 3401 2005. pp. 424-431
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