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

研究成果: Conference contribution

抜粋

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.

元の言語English
ホスト出版物のタイトル1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992
出版者Institute of Electrical and Electronics Engineers Inc.
ページ2773-2776
ページ数4
ISBN(電子版)0780305930
DOI
出版物ステータス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(印刷物)0271-4310

Conference

Conference1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992
United States
San Diego
期間92/5/1092/5/13

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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  • これを引用

    Oishi, SI. (1992). The self-validating numerics - A new tool for computer assisted proofs of nonlinear problems. : 1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992 (pp. 2773-2776). [230623] (Proceedings - IEEE International Symposium on Circuits and Systems; 巻数 6). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISCAS.1992.230623