A modified Newton method with guaranteed accuracy based on rational arithmetic

Akira Inoue, Masahide Kashiwagi, Shin'ichi 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 1

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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