Chaos in Newtonian iterations: Searching for zeros which are not there
Chaotic Dynamics
2011-01-24 v1
Abstract
We show analytically that Newtonian iterations, when applied to a polynomial equation, have a positive topological entropy. In a specific example of an attempt to ``find'' the real solutions of the equation , we show that the Newton method is chaotic. We analytically find the invariant density and show how this problem relates to that of a piecewise linear map.
Cite
@article{arxiv.nlin/0703061,
title = {Chaos in Newtonian iterations: Searching for zeros which are not there},
author = {Lukasz Skowronek and P. F. Gora},
journal= {arXiv preprint arXiv:nlin/0703061},
year = {2011}
}