Let $a$ be a positive real number, and let the sequence of real numbers $x_i$ be given by

$x_0=1,x_{i+1}=\frac{1}{2}**(x_i+\frac{a}{x_i})$

The value $x_i$ will converge to $\sqrt[\phantom{2}]{a}$ as $i$ Write a program that reads in the value of $a$

interactively and uses this algorithm to compute the square root of $a.$

Test your program as you vary the maximum number of iterations of the algorithm is increased

from $1,2,3,$dots and determine how many significant digits of precision that you obtain for each.

How many iterations are necessary to reach the machine precision of matlab? By Mathmatical Solution