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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Newton's method and symbolic dynamics


Author: Sherman Wong
Journal: Proc. Amer. Math. Soc. 91 (1984), 245-253
MSC: Primary 65H05; Secondary 58F12
MathSciNet review: 740179
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Abstract: By the use of symbolic dynamics, this note proves a result of B. Barna concerning real polynomials of degree at least 4 and having all distinct simple real roots. Specifically, the set of initial points, for which Newton's method fails to converge to a root of the given polynomial, is homeomorphic to a Cantor set. Also the note shows that the requirement for simple roots may be relaxed, and one still has Barna's result being valid.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740179-6
PII: S 0002-9939(1984)0740179-6
Keywords: Newton's method, symbolic dynamics
Article copyright: © Copyright 1984 American Mathematical Society