Newton's method's basins of attraction revisited
arXiv:1708.0273250 citations
Originality Synthesis-oriented
AI Analysis
Provides a visual demonstration of chaotic convergence behavior in Newton's method for mathematicians and numerical analysts.
The paper revisits Newton's method's convergence behavior, showing that even a simple modified version exhibits complex, parameter-dependent convergent regions.
In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions, i.e. regions where the method converges nicely to a root, can be complicatedly a function of the parameter.