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Order of Convergence: Iteration Scheme

  • Thread starter noodleface
  • Start date
  • #1

Homework Statement


I have attached the actual problem as a picture (hope that is ok).

Xn+1 = 12/(1+Xn), r=3

For each of the following iteration schemes the sequence xn will converge to the given value of r provided the
initial value x0 is sufficiently close to r. In each case determine the order of convergence.


Homework Equations



I have the equation:

|en+1/enα| ≈ C

en = r - xn
en+1 = r - xn+1

The Attempt at a Solution



I have attempted to substitute xn+1 into the last equation and then divided terms, but I end up with a final result of 3/(1+xn). I cannot understand how to find the order of convergence from this. Any hints would be appreciated.
 

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