The fixed$-$point iteration method to find the root of an equation has the follow scheme

$x_{i+1}=g(x_i)$

where $x=g(x)$ is derived from $f(x)=0.$ An improved fixed$-$point iteration scheme can be

proposed as follows

$y_i=g(x_i),z_i=g(y_i),$ and $x_{i+1}=x_i-\frac{(y_i-x_i{)}^2}{z_i-2y_i+x_i}$

Modify the given M$-$file function FixedPointIter.m and create a new M$-$file function

FixedPointAcc. $m$ by implementing the improved fixed$-$point iteration method. Test the new

function with the example problem given in the lecture, that is to locate the root of $f(x)=e^{-x}-x.$

Compare your iteration results with the ones yielded from the conventional fixed$-$point iteration

method. You can assume $x_0=0,g(x)=e^{-x}$ and ${}_s=0\mathrm{.}1\%.[20$ pts$]$