Continuous Newton Method

December 27th, 2016

\(\dot{s}(t) = -\frac{p(s(t))}{p'(s(t))}\)
\(p(z) = z^4 - 3z^2 + 3\)

What if we treat Newton's method as a differential equation? This is called the "continuous" Newton's method. Unlike the usual Newton's method, this is much more stable. The tradeoff is of course, that it is much more computationally intensive.

Here we see the trajectories of 64 points as they move according to the formulas above.