Newton's Method as a Dynamical System: Global Convergence and Predictability.
Memorandum rept. 15 Sep 83-15 Sep 84,
NAVAL RESEARCH LAB WASHINGTON DC
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Newtons method as an iterative scheme to compute both unstable and stable fixed points of a discrete dynamical system is considered. It is shown for Newton iterations that the basins of attraction are intertwined in a complicated manner. This complex structure appears to be fractal, and its dimension is estimated. Consequences of predictability for the final state are given in terms of imprecision in the initial data. Keywords include Newtons method, Predictability, Basin boundaries, Fractal, Nonlinear dynamic.
- Numerical Mathematics