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 Sin(x) function. The iterate derived in the previous post is as follows

x(n+1) = x(n) - Tan(x(n))

If one start at start around 2 we quickly converge to the solution. 🙂

The sin function is shown in multicolours, the map is in black.

But what happens when we start near a point where derivative of the sin function is zero ? It goes into oblivion.

Moral of the story is if you are using newtons iteration one must be careful if the derivative of the function is nearly zero.

To be continued.

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