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

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- Dec 10th 2008, 01:05 PMMandelbrotFinding 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, 01:41 PMCaptainBlack
You need to find starting points close to each root, they are close to $\displaystyle x=-1.3,\ x=2.0,\ x=3.8$. Then use standard Newtons method starting from each.

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

CB - Dec 11th 2008, 01:22 PMMandelbrot
thank u CB,I will have to study with these roots now,then I'll think about iteration..

thank u so much