How do I modify this bracketing bisection method from a 'for' loop to a 'while loop'??

This is a bisection method for root finding the function ?(?) = ?^2 − 3. 

• Modify this file from a ‘for’ loop to a while loop that has a stopping criterion when the percent relative error (obtained by multiplying the εa equation below by 100) is less than 0.01%. How many iterations did this code perform to obtain a result within 0.01% of the actual root? (Hint: remove the pause(1) line to make the algorithm run as fast as it can).

% Bracketing Bisection Method
clear all
close all
x=linspace(1,5,300)
y = x.^2-3
i=1
xl(i) = min(x)
xu(i) = max(x)
yl(i) = xl(i).^2-3
yu(i) = xu(i).^2-3
if yl(i)*yu(i)<0
for i=2:20
subplot(1,2,1)
plot(x,y,'k');hold on
plot([1 5],[0 0],'k--')
    xr(i) = (xl(i-1)+xu(i-1))./2;
    yr(i) = xr(i).^2-3;
    yu(i) = xu(i-1).^2-3;
    yl(i) = xl(i-1).^2-3;
    
    prodleft = yl(i)*yr(i);
    prodright = yr(i)*yu(i);
    
   if  prodleft <0
       xu(i) = xr(i);
       xl(i) = xl(i-1);
   else
       xl(i) = xr(i);
       xu(i) = xu(i-1);
   end
   subplot(1,2,1)
   plot([xl(i) xl(i)],[-5 25],'r:');
   plot([xu(i) xu(i)],[-5 25],'r:');
   axis([1 3 -2 5])
   title('x_r per iteration','Fontsize',20)
   xlabel('x','Fontsize',20)
   ylabel('f(x)','Fontsize',20)
   axis square
   hold off
   subplot(1,2,2)
   plot(xr)
   xlim([0 20])
   title('x_r','Fontsize',20)
   xlabel('Iteration number [-]','Fontsize',20)
   ylabel('x_r','Fontsize',20)
   axis square
pause(1)
end
end
       

Answer 1

[darova]

Solution