Help with simple bisection method function while loop

I am writing a simple root finding bisection method function using a while loop and can't seem to get it to cycle through once i get first correction. Any help is much appreciated.

function [x] = bisection2(x1,x2,tol)
%UNTITLED2 Summary of this function goes here


f=@(x) cos((pi/2)*x)/(1-x^2);

x= (x1+x2)/2;

p=f(x);

i=0;


 if p<=tol
     fprintf('A Root at x = %f was found in 1 iterations with an error of \n' , x,i)
        return
 end
while p > tol
    
    i= i+1;

x= (x1+x2)/2;

p=f(x);
   
    
    if sign(p)==sign(f(x1))
        x1=x;
         fprintf('Iteration: %f x tested: %f Error Found: %f \n',i,x,p)
        return
    end
        if sign(p)== sign(f(x2))
            x2=x;
             fprintf('Iteration: %f x tested: %f Error Found: %f \n',i,x,p)
            return
        else
            disp('Root not Bounded!')
            return 
        end
   
end
    
end

Answer 1

[Steven Lord]

Let's say your function was:

f = @(x) -x.^2;

and your tolerance was 1e-6. Is the tolerance satisfied if I evaluate f at x = 1?

tol = 1e-6

tol = 1.0000e-06

y = f(1)

y = -1

isYSmallerThanTol = y < tol

isYSmallerThanTol = logical
   1

So good enough, I've found my root, right?