# Finding roots with Newton's method

• Dec 10th 2008, 02:05 PM
Mandelbrot
Finding roots with Newton's method
How can I find three roots of F(x)=cosx+0.2x with newton's method?
And,for all roots;I need take n(iteration number) ,but how can I identify iteration number?

thanks so much
• Dec 10th 2008, 02:41 PM
CaptainBlack
Quote:

Originally Posted by Mandelbrot
How can I find three roots of F(x)=cosx+0.2x with newton's method?
And,for all roots;I need take n(iteration number) ,but how can I identify iteration number?

thanks so much

You need to find starting points close to each root, they are close to $x=-1.3,\ x=2.0,\ x=3.8$. Then use standard Newtons method starting from each.

You don't normaly precompute how many itterations you need, but keep going untill $|x_{n+1}-x_n|$ is less than some preset tolerance.

CB
• Dec 11th 2008, 02:22 PM
Mandelbrot
thank u CB,I will have to study with these roots now,then I'll think about iteration..

thank u so much