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

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

Abstract

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.

Original languageEnglish
Title of host publication1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2773-2776
Number of pages4
ISBN (Electronic)0780305930
DOIs
Publication statusPublished - 1992
Event1992 IEEE International Symposium on Circuits and Systems, ISCAS 1992 - San Diego, United States
Duration: 1992 May 101992 May 13

Publication series

NameProceedings - IEEE International Symposium on Circuits and Systems
Volume6
ISSN (Print)0271-4310

Conference

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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