Calc the # of steps Newton's Method takes to reach Tolerance

[david__taylor]

I need to calculate the number of steps required to reach a specified accuracy by using the Newton method. Here is the question:

\(\displaystyle Newton: |x_{n+1} - r| \leq C_{nwt}. |x_n - r|^{2}\)
If an initial guess, \(\displaystyle x_0\), is supplied such that \(\displaystyle |x_n - r| = 10^{-2}\), and we assume that \(\displaystyle C_{nwt} = 7\), how many steps of each method are necessary to ensure that \(\displaystyle |x_n - r| \leq 10^{-14}\)?

N.B. roots of multiplicity one.


Hope someone can help!

Thanks

 

[Deleted member 4993]

I need to calculate the number of steps required to reach a specified accuracy by using the Newton method. Here is the question:

\(\displaystyle Newton: |x_{n+1} - r| \leq C_{nwt}. |x_n - r|^{2}\)
If an initial guess, \(\displaystyle x_0\), is supplied such that \(\displaystyle |x_n - r| = 10^{-2}\), and we assume that \(\displaystyle C_{nwt} = 7\), how many steps of each method are necessary to ensure that \(\displaystyle |x_n - r| \leq 10^{-14}\)?

N.B. roots of multiplicity one.


Hope someone can help!

Thanks

Try to calculate by hand the ratio of x[sub:3bp7d9cg]n[/sub:3bp7d9cg]step to x[sub:3bp7d9cg]n+1[/sub:3bp7d9cg] as a function of C[sub:3bp7d9cg]nwt[/sub:3bp7d9cg] and x[sub:3bp7d9cg]n[/sub:3bp7d9cg]

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.