create a function file in matlab that performs fixedpoint it

create a function file in matlab that performs fixed-point iteration to find the roots of a function. Test your code for the following functions. your inputs should be the g formula, its derivative, an intial guess, and tolerance. your code must also take convergence into consideration.

x³ -x²= x

cos(x)=x

Solution

clc
clear;
disp(\'x=x^3-x^2\');
x=0.1;
tol=1;
itr=0;
while(tol>0.000001),
xi=x^3-x^2;
tol=abs(x-xi);
x=xi;
itr=itr+1;
end
itr
x
disp(\'x=cos(x)\');
x=0.1;
tol=1;
itr=0;
while(tol>0.000001),
xi=cos(x);
tol=abs(x-xi);
x=xi;
itr=itr+1;
end
itr
x

result:

x=x^3-x^2

itr =

     4

x =

-4.4625e-17

x=cos(x)

itr =

    35

x =

    0.7391