An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces

Shinichi Oishi, Masahide Kashiwagi, Mitsunori Makino, Kazuo Horiuchi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A constructive simplified Newton method is presented for calculating solutions of infinite dimensional nonlinear equations, which uses a projection scheme from an infinite dimensional space to finite dimensional subspaces. A convergence theorem of the method is shown based on Urabe's theorem. For a class of successive approximation methods containing an infinite dimensional homotopy method, a stopping criterion is shown using the convergence theorem. The authors show that under a certain condition the stopping criterion is satisfied in finite cycles of iteration.

Original languageEnglish
Title of host publicationProceedings - IEEE International Symposium on Circuits and Systems
PublisherPubl by IEEE
Pages1236-1239
Number of pages4
Volume2
Publication statusPublished - 1991
Externally publishedYes
Event1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5) - Singapore, Singapore
Duration: 1991 Jun 111991 Jun 14

Other

Other1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5)
CitySingapore, Singapore
Period91/6/1191/6/14

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ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials

Cite this

Oishi, S., Kashiwagi, M., Makino, M., & Horiuchi, K. (1991). An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces. In Proceedings - IEEE International Symposium on Circuits and Systems (Vol. 2, pp. 1236-1239). Publ by IEEE.