The self-validating numerics - A new tool for computer assisted proofs of nonlinear problems

Shin'Ichi Oishi*

*この研究の対応する著者

研究成果: Conference contribution

抄録

The self-validating numerical method is sueveyed for nonlinear problems. By taking into account of the effect of rounding error rigorously, this method provides a method of computer assisted proofs. In the first place, Kantrovich's approach to this problem is surveyed. His method is based on his convergence theorem of Newton's method and can be seen as an a posteriori error estimation method. Then, Urabe's approach to this problem is discussed. He treated practical nonlinear differential equations such as the van der Pol equation and the Duffing equation and proved the existence of their periodic and quasi-periodic solutions by the self-validating numerics. Generalizations and abstraction of Urabe's method to more general functional equations is also discussed. Then methods for rigorous estimation of rounding errors are surveyed.

本文言語English
ホスト出版物のタイトル1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992
出版社Institute of Electrical and Electronics Engineers Inc.
ページ2773-2776
ページ数4
ISBN(電子版)0780305930
DOI
出版ステータスPublished - 1992
イベント1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992 - San Diego, United States
継続期間: 1992 5 101992 5 13

出版物シリーズ

名前Proceedings - IEEE International Symposium on Circuits and Systems
6
ISSN(印刷版)0271-4310

Conference

Conference1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992
国/地域United States
CitySan Diego
Period92/5/1092/5/13

ASJC Scopus subject areas

  • 電子工学および電気工学

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