MATLAB write:

Use Newtons method to compute sqrt(R) in double precision by

a) xn+1 = (xn+R/xn)

b) xn+1 = [xn(xn2+3R)]/[3xn2+R]

For R = 0.001, 0.1, 10, and 1000 with a stopping criteria of 1) |xn+1-xn|< 10-14 2) |xn+1-xn|< 10-6.

i) Record the number of iterations required to reach the stopping criteria for each of the two methods for each value of R. ii) Plot the values of xn for methods a) and b) in the same plot with separate plots for the different R values.

iii) How sensitive are the iteration counts to your selected starting value?

iv) Which method converge the fastest?

v) Why?