TY - JOUR

T1 - A modified Newton method with guaranteed accuracy based on rational arithmetic

AU - Inoue, Akira

AU - Kashiwagi, Masahide

AU - Oishi, Shin'ichi

AU - Makino, Mitsunori

PY - 1993/5/1

Y1 - 1993/5/1

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:0027601642

SN - 0916-8508

VL - E76-A

SP - 795

EP - 805

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

IS - 5

ER -