Example 6. Convergence: Spiral  Find the solution to  .  Use the starting approximation    

Solution 6.

Since   for all   ,  the iteration    will converge to the fixed point  .  In this case,   is said to be an attractive fixed point.  

Animation 3.  ( Fixed Point Iteration  Fixed Point Iteration ).  Internet hyperlink.

(c) John H. Mathews 2004