Given the function f(x) =1 + 0.5 sin x, show that it has a unique fixed point x* in the interval I=[0,2] and that the iterations xn+1=f(xn) converge to the fixed point for any x0 Є I.
Also, find the number of iterations necessary to guarantee that |xn - x* | < 10^-2 .
Write a short Matlab code to find the fixed point.
A fixed point iteration problem is solved using Matlab. The solution is detailed and well presented.