CarmineCortez
Sep29-09, 11:57 AM
1. The problem statement, all variables and given/known data
Suppose that f(x) = 0 at x = p and f'(p)!=0 and f''(p) = 0, show that Newton's method converges by at least order 3.
3. The attempt at a solution
I used a Taylor's series expansion. Got: f(x) = f'(p)(x-p) + (f'''(p)(x-p)^3)/3!
then let x = p_n and by using the mean value thm.
f(p_n) = f(p_n) - f(p) + (f'''(p)(x-p)^3)/3!
and then everything goes to 0...so is there a mistake?
thanks
Suppose that f(x) = 0 at x = p and f'(p)!=0 and f''(p) = 0, show that Newton's method converges by at least order 3.
3. The attempt at a solution
I used a Taylor's series expansion. Got: f(x) = f'(p)(x-p) + (f'''(p)(x-p)^3)/3!
then let x = p_n and by using the mean value thm.
f(p_n) = f(p_n) - f(p) + (f'''(p)(x-p)^3)/3!
and then everything goes to 0...so is there a mistake?
thanks