Algorithm for finding all solutions of parameter-dependent nonlinear equations with guaranteed accuracy

Yuchi Kanzawa, Masahide Kashiwagi, Shin'ichi Oishi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper proposes an algorithm which can derive all solutions with guaranteed accuracy for equations including a nonlinear function, with the dimension of the domain larger than the dimension of the range. It is mathematically shown that the proposed algorithm is completed in a finite number of steps under an appropriate condition. The effectiveness of the proposed algorithm is demonstrated by numerical examples.

Original languageEnglish
Pages (from-to)33-39
Number of pages7
JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
Volume82
Issue number10
DOIs
Publication statusPublished - 1999 Oct
Externally publishedYes

Fingerprint

Nonlinear equations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

@article{2ca8e98b29d34b03af7f00da8484e36a,
title = "Algorithm for finding all solutions of parameter-dependent nonlinear equations with guaranteed accuracy",
abstract = "This paper proposes an algorithm which can derive all solutions with guaranteed accuracy for equations including a nonlinear function, with the dimension of the domain larger than the dimension of the range. It is mathematically shown that the proposed algorithm is completed in a finite number of steps under an appropriate condition. The effectiveness of the proposed algorithm is demonstrated by numerical examples.",
author = "Yuchi Kanzawa and Masahide Kashiwagi and Shin'ichi Oishi",
year = "1999",
month = "10",
doi = "10.1002/(SICI)1520-6440(199910)82:10<33::AID-ECJC5>3.0.CO;2-F",
language = "English",
volume = "82",
pages = "33--39",
journal = "Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)",
issn = "1042-0967",
publisher = "John Wiley and Sons Inc.",
number = "10",

}

TY - JOUR

T1 - Algorithm for finding all solutions of parameter-dependent nonlinear equations with guaranteed accuracy

AU - Kanzawa, Yuchi

AU - Kashiwagi, Masahide

AU - Oishi, Shin'ichi

PY - 1999/10

Y1 - 1999/10

N2 - This paper proposes an algorithm which can derive all solutions with guaranteed accuracy for equations including a nonlinear function, with the dimension of the domain larger than the dimension of the range. It is mathematically shown that the proposed algorithm is completed in a finite number of steps under an appropriate condition. The effectiveness of the proposed algorithm is demonstrated by numerical examples.

AB - This paper proposes an algorithm which can derive all solutions with guaranteed accuracy for equations including a nonlinear function, with the dimension of the domain larger than the dimension of the range. It is mathematically shown that the proposed algorithm is completed in a finite number of steps under an appropriate condition. The effectiveness of the proposed algorithm is demonstrated by numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=0032654837&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032654837&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1520-6440(199910)82:10<33::AID-ECJC5>3.0.CO;2-F

DO - 10.1002/(SICI)1520-6440(199910)82:10<33::AID-ECJC5>3.0.CO;2-F

M3 - Article

AN - SCOPUS:0032654837

VL - 82

SP - 33

EP - 39

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 - 10

ER -