Regula-falsi Method that keeps running

I have this script for Regula-Falsi Method to get a root of a function but it just keeps running. Anyone can help find what's wrong?

f = @(x) 2.^x - x.^2 - 2; % Function whose roots are desired

xL = 4; xU = 5; % Initial guesses

Tol = 1e-6; % Tolerance (0.000001)

c = 0; % Counter for the no. of iterations

while abs( xU-xL ) > Tol

c = c + 1

xm = xU-f(xU)* (xU-xL)/f(xU)- f(xL); % Compute xm

fm = f(xm); % Evaluate the function at x = xm

% % Print the intermediate results

fprintf('Iteration: %d\t',c);

fprintf ('[xL,xU,xm ] = [%.6f, %.6f, %.6f]\n', xL,xU,xm);

if f(xL ) *fm < 0 % If the root is on the left,

xU = xm ; % then set xm as the new xU.

elseif fm * f( xU ) < 0 % But if the root is on the

xL = xm ; % then set xm as the new xL.

else

break; % Stop! xm is exactly the root

end

end

plot(xm,f(xm),'r*', 'Markersize', 10); % plot the xm points

fprintf ('The root is: %.6f \n', xm);

Answer 1

[Alan Stevens]

Brackets!!

f = @(x) 2.^x - x.^2 - 2; % Function whose roots are desired
xL = 4; xU = 5;             % Initial guesses
Tol = 1e-6; % Tolerance (0.000001)
c = 0; % Counter for the no. of iterations
while abs( xU-xL ) > Tol
    c = c + 1;
    xm = xU-f(xU)* (xU-xL)/(f(xU)- f(xL)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Put brackets round f(xU)-f(xL)
    fm = f(xm);                          % Evaluate the function at x = xm
    
%     % Print the intermediate results
 fprintf('Iteration: %d\t',c);
fprintf ('[xL,xU,xm ] = [%.6f, %.6f, %.6f]\n', xL,xU,xm);
    if f(xL ) *fm < 0               % If the root is on the left,
        xU = xm ;                   % then set xm as the new xU.
    elseif fm * f( xU ) < 0         % But if the root is on the
        xL = xm ;                   % then set xm as the new xL.
    else
        break;                      % Stop! xm is exactly the root
    end
end

Iteration: 1	

[xL,xU,xm ] = [4.000000, 5.000000, 4.285714]

Iteration: 2	

[xL,xU,xm ] = [4.285714, 5.000000, 4.390866]

Iteration: 3	

[xL,xU,xm ] = [4.390866, 5.000000, 4.425434]

Iteration: 4	

[xL,xU,xm ] = [4.425434, 5.000000, 4.436351]

Iteration: 5	

[xL,xU,xm ] = [4.436351, 5.000000, 4.439754]

Iteration: 6	

[xL,xU,xm ] = [4.439754, 5.000000, 4.440811]

Iteration: 7	

[xL,xU,xm ] = [4.440811, 5.000000, 4.441138]

Iteration: 8	

[xL,xU,xm ] = [4.441138, 5.000000, 4.441240]

Iteration: 9	

[xL,xU,xm ] = [4.441240, 5.000000, 4.441271]

Iteration: 10	

[xL,xU,xm ] = [4.441271, 5.000000, 4.441281]

Iteration: 11	

[xL,xU,xm ] = [4.441281, 5.000000, 4.441284]

Iteration: 12	

[xL,xU,xm ] = [4.441284, 5.000000, 4.441285]

Iteration: 13	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 14	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 15	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 16	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 17	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 18	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 19	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 20	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 21	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 22	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 23	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 24	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 25	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 26	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 27	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 28	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 29	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

Iteration: 30	

[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]

plot(xm,f(xm),'r*', 'Markersize', 10); % plot the xm points

fprintf ('The root is: %.6f \n', xm);

The root is: 4.441285 

[BG]

Thank you so much. I didn't see that.