Imperfect singular solutions of nonlinear equations and a numerical method of proving their existence

Yuchi Kanzawa, Shin'Ichi Oishi

Research output: Contribution to journalArticle

6 Citations (Scopus)


A new concept of "an imperfect singular solution" is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration.

Original languageEnglish
Pages (from-to)1062-1069
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number6
Publication statusPublished - 1999 Jan 1



  • Imperfect singular solutions extended systems
  • Krawczyk-based interval validation method
  • Numerical computation with guaranteed accuracy

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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