- #1
John Harris
- 19
- 1
Homework Statement
For which of them will the corresponding fixed point iteration xk+1 = g(xk) be locally convergent to the solution xbar in [0, 1]? (The condition to check is whether |g'(xbar)| < 1.)
A) 1/x2 -1
B)...
C)...
compute xbar to within absolute error 10-4.
Homework Equations
3. The Attempt at a Solution
I[/B] don't think I understand the question in general terms, but this is what I think I have to do.
The solution xbar is 1 because g(1)=0. It's not locally convergent because |g'(1)|=-2
Since xbar isn't locally convergent I can't computer xbar. But calculating it would look like:
k | xk
1 1
2 -2
3 .25
4 128
Can you please help me understand what this problem is asking for, or similar examples of this problem, or what I'm doing wrong. Thank you