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
- 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