### Abstract

This paper proposes an algorithm with a guaranteed accuracy for the finite-dimensional nonlinear equation. First, an algorithm is shown which can determine the interval containing the true solution, based on the given approximate solution. The method is based on the interval analysis and considers the representation error of the equation. Then the interval iteration method is shown which can arbitrarily reduce the interval. The rational number arithmetic is used and the rounding of the rational number is utilized effectively. Finally, an experimental implementation of the algorithm on a computer is presented, together with some numerical examples.

Original language | English |
---|---|

Pages (from-to) | 99-112 |

Number of pages | 14 |

Journal | Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi) |

Volume | 78 |

Issue number | 7 |

Publication status | Published - 1995 Jul |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

**Numerical validation method for nonlinear equations using interval analysis and rational arithmetic.** / Kashiwagi, Masahide; Oishi, Shinichi.

Research output: Contribution to journal › Article

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*, vol. 78, no. 7, pp. 99-112.

}

TY - JOUR

T1 - Numerical validation method for nonlinear equations using interval analysis and rational arithmetic

AU - Kashiwagi, Masahide

AU - Oishi, Shinichi

PY - 1995/7

Y1 - 1995/7

N2 - This paper proposes an algorithm with a guaranteed accuracy for the finite-dimensional nonlinear equation. First, an algorithm is shown which can determine the interval containing the true solution, based on the given approximate solution. The method is based on the interval analysis and considers the representation error of the equation. Then the interval iteration method is shown which can arbitrarily reduce the interval. The rational number arithmetic is used and the rounding of the rational number is utilized effectively. Finally, an experimental implementation of the algorithm on a computer is presented, together with some numerical examples.

AB - This paper proposes an algorithm with a guaranteed accuracy for the finite-dimensional nonlinear equation. First, an algorithm is shown which can determine the interval containing the true solution, based on the given approximate solution. The method is based on the interval analysis and considers the representation error of the equation. Then the interval iteration method is shown which can arbitrarily reduce the interval. The rational number arithmetic is used and the rounding of the rational number is utilized effectively. Finally, an experimental implementation of the algorithm on a computer is presented, together with some numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=0029332340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029332340&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0029332340

VL - 78

SP - 99

EP - 112

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 7

ER -