Shadowing orbits and Kantorovich's theorem

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1996Publisher:Springer Science and Business Media LLCJournal:Numerische Mathematik, volume 73, pages 65-73 (issn: 0029-599X, eissn: 0945-3245,

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Authors: Hadeler, K. P.;

doi: 10.1007/s002110050184

Shadowing orbits and Kantorovich's theorem

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Abstract

The author points out the close connection between Kantorovich's theorem on convergence of Newton's method and the existence of a finite shadowing orbit of a given pseudo-orbit. This paper clarifies some results that are already known and simplifies their proofs.

Related Organizations

University of Tübingen
Germany

Keywords

pseudo-orbits, shadowing lemma, Newton's method, Numerical solutions to equations with nonlinear operators, Low-dimensional dynamical systems

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