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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Newton-Raphson method
Nonlinear equations

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.

An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces. / Oishi, Shinichi; Kashiwagi, Masahide; Makino, Mitsunori; Horiuchi, Kazuo.

Proceedings - IEEE International Symposium on Circuits and Systems. Vol. 2 Publ by IEEE, 1991. p. 1236-1239.

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

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, Publ by IEEE, pp. 1236-1239, 1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5), Singapore, Singapore, 91/6/11.
Oishi S, Kashiwagi M, Makino M, Horiuchi K. 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. Publ by IEEE. 1991. p. 1236-1239
Oishi, Shinichi ; Kashiwagi, Masahide ; Makino, Mitsunori ; Horiuchi, Kazuo. / An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces. Proceedings - IEEE International Symposium on Circuits and Systems. Vol. 2 Publ by IEEE, 1991. pp. 1236-1239
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