A modified Newton method with guaranteed accuracy based on rational arithmetic

Akira Inoue*, Masahide Kashiwagi, Shin'ichi Oishi, Mitsunori Makino


研究成果: Article査読


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.

ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
出版ステータスPublished - 1993 5月 1

ASJC Scopus subject areas

  • 信号処理
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 電子工学および電気工学
  • 応用数学


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