Dynamical Systems · Optimization

Newtons iteration as a map – Part 2

It is fun to look at how the iterates move in newton's iterations in the case of $latex Sin(x) $ function. The iterate derived in the previous post is as follows $latex x(n+1) = x(n) - Tan(x(n)) $ If one start at start around 2 we quickly converge to the solution. 🙂 The sin function… Continue reading Newtons iteration as a map – Part 2

Dynamical Systems · Optimization

Newton’s iteration as map – Part 1

Newton Iterations is a well known methodology to compute the solution of the problem f(x) = 0. It is very interesting to look at it as a map. The iteration step is as follows for x(n+1). Let the function be Sin(x) then it results in the following map The plot of the function and the… Continue reading Newton’s iteration as map – Part 1

Dynamical Systems · Machine Learning

Mathematica for machine learning – Learning a map

Mathematica newly introduced machine learning to its kitty. And I was excited to see its capabilities! So I decided to test its RNN abilities..to begin with (Really RNN!). So here is a simple problem for Mathematica's RNN chain to learn - A simple map 2x Mod 1. You start with a number say 'x' the… Continue reading Mathematica for machine learning – Learning a map