Example 1 64 outlined the following algorithm for computing the square root of 2 Verify that cent The function f(x) 1 2 (x 2 x) is contraction mapping on the set X x x yen 1 cent The fixed point of f is 2 Estimate how many iterations are required to ensure that the approximation error is less than ...

First observe that 1 for every 1 Therefore For any Since 1 1 for all so that or 12 is a co ...

Example 1.64 outlined the following algorithm for computing the square root of 2: Verify that ¢ The

Question:

Example 1.64 outlined the following algorithm for computing the square root of 2:

Verify that
€¢ The function f(x) = 1/2 (x + 2/x) is contraction mapping on the set X = {x ˆŠ „œ: x ‰¥ 1}
€¢ The fixed point of f is ˆš2
Estimate how many iterations are required to ensure that the approximation error is less than 0.001.
The following result is often useful in establishing the properties of the fixed point of a particular model.