Newton’s method and symbolic dynamics

Wong, Sherman

doi:10.1090/S0002-9939-1984-0740179-6

Newton's method and symbolic dynamics

Author: Sherman Wong
Journal: Proc. Amer. Math. Soc. 91 (1984), 245-253
MSC: Primary 65H05; Secondary 58F12
DOI: https://doi.org/10.1090/S0002-9939-1984-0740179-6
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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