Some reflections on Newton's method

F. Twilt

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    Abstract

    An infinitesimal version (Newton flow) of Newton’s iteration for finding zeros of rational functions on the complex plane is introduced. Structural stability aspects are discussed, including a characterization and classification of structurally stable Newton flows in terms of certain plane graphs. Possible generalizations to other classes of functions are indicated and several open problems are posed.
    Original languageEnglish
    Title of host publicationTopics in Engineering Mathematics
    Subtitle of host publicationModeling and Methods
    EditorsAdriaan van der Burgh, Juriaan Simonis
    PublisherKluwer Academic Publishers
    Pages217-237
    ISBN (Electronic)978-94-011-1814-9
    ISBN (Print)978-94-010-4800-2
    DOIs
    Publication statusPublished - 1992

    Publication series

    NameMathematics and Its Applications
    PublisherKluwer Academic Publishers
    Volume81

    Keywords

    • METIS-140991
    • Newton flow
    • structural stability
    • rational function

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