Not really sure where to post this question, but here we go.
I need to compute the first several iterations of Newtonīs method for solving
, using initial guess .
First things first. How would this be set up?
Would this give me:
If so, how do I decide in general the apparent convergence rate?
What should the asymptotic convergence rate be?
How many iterations are required before the asymptotic convergence is reached?
Finally, give an analytical explanation of the behavior one observes.
I donīt even know what asymptotic convergence is.
So if my function was instead , then:
Which behaves like if is large ?
Is my rate of convergence linear here also?
Will the error on the n-th iteration be the constant 2/3 times the error on the n-1 th iteration ?
PS: Any good links to pages about this subject?