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.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s