A modified Newton method with guaranteed accuracy based on rational arithmetic

Akira Inoue, Masahide Kashiwagi, Shinichi Oishi, Mitsunori Makino

    Research output: Contribution to journalArticle

    Abstract

    In this paper, we are concerned with a problem of obtaining an approximate solution of a finite-dimensional nonlinear equation with guaranteed accuracy. Assuming that an approximate solution of a nonlinear equation is already calculated by a certain numerical method, we present computable conditions to validate whether there exists and exact solution in a neighborhood of this approximate solution or not. In order to check such conditions by computers, we present a method using rational arithmetic. In this method, both the effects of the truncation errors and the rounding errors of numerical computation are taken into consideration. Moreover, based on rational arithmetic we propose a new modified newton iteration to obtain an improved approximate solution with desired accuracy.

    Original languageEnglish
    Pages (from-to)795-805
    Number of pages11
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE76-A
    Issue number5
    Publication statusPublished - 1993 May

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    Modified Newton Method
    Newton-Raphson method
    Nonlinear equations
    Approximate Solution
    Numerical methods
    Nonlinear Equations
    Newton Iteration
    Rounding error
    Truncation Error
    Numerical Computation
    Exact Solution
    Numerical Methods

    ASJC Scopus subject areas

    • Hardware and Architecture
    • Information Systems
    • Electrical and Electronic Engineering

    Cite this

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    AU - Kashiwagi, Masahide

    AU - Oishi, Shinichi

    AU - Makino, Mitsunori

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