Bisection method add iteration table into my code

function  m = bisection(f, low, high, tol)
disp('Bisection Method'); 
% Evaluate both ends of the interval
y1 = feval(f, low);
y2 = feval(f, high);
i = 0; 
% Display error and finish if signs are not different
if y1 * y2 > 0
   disp('Have not found a change in sign. Will not continue...');
   return
end 
% Work with the limits modifying them until you find
% a function close enough to zero.
disp('Iter    low        high          x0');
while (abs(high - low) >= tol)
    i = i + 1;
    % Find a new value to be tested as a root
    m = (high + low)/2;
    y3 = feval(f, m);
    if y3 == 0
        fprintf('Root at x = %f \n\n', m);
        return
    end
    fprintf('%2i \t %f \t %f \t %f \n', i-1, low, high, m);   

      % Update the limits
      if y1 * y3 > 0
          low = m;
          y1 = y3;
      else
          high = m;
      end
  end 

% Show the last approximation considering the tolerance
w = feval(f, m);
fprintf('\n x = %f produces f(x) = %f \n %i iterations\n', m, y3, i-1);
fprintf(' Approximation with tolerance = %f \n', tol);

If it is important my code works by entering variables into command line like:

my_fun = @(x) exp(x) - 3*x;
low = 0;
high = 1;
tolerance = .00001;
x = bisection(my_fun, low, high, tolerance);

I want to ask how could I add an iterations graphic into my code? I want to see a x value at each iteration.

Answer 1

[Alan Stevens]

Something like this?

my_fun = @(x) exp(x) - 3*x;
low = 0;
high = 1;
tolerance = .00001;
[x, x0] = bisection(my_fun, low, high, tolerance); %%%%%%%%%%%%%%%%%

Bisection Method
Iter    low        high          x0
 0 	 0.000000 	 1.000000 	 0.500000 
 1 	 0.500000 	 1.000000 	 0.750000 
 2 	 0.500000 	 0.750000 	 0.625000 
 3 	 0.500000 	 0.625000 	 0.562500 
 4 	 0.562500 	 0.625000 	 0.593750 
 5 	 0.593750 	 0.625000 	 0.609375 
 6 	 0.609375 	 0.625000 	 0.617188 
 7 	 0.617188 	 0.625000 	 0.621094 
 8 	 0.617188 	 0.621094 	 0.619141 
 9 	 0.617188 	 0.619141 	 0.618164 
10 	 0.618164 	 0.619141 	 0.618652 
11 	 0.618652 	 0.619141 	 0.618896 
12 	 0.618896 	 0.619141 	 0.619019 
13 	 0.619019 	 0.619141 	 0.619080 
14 	 0.619019 	 0.619080 	 0.619049 
15 	 0.619049 	 0.619080 	 0.619064 
16 	 0.619049 	 0.619064 	 0.619057 

 x = 0.619057 produces f(x) = 0.000005 
 16 iterations
 Approximation with tolerance = 0.000010 

plot(0:numel(x0)-1,x0,'*--'),grid %%%%%%%%%%%%%%%%%%%%%%%%

function  [m, x0] = bisection(f, low, high, tol)
disp('Bisection Method'); 
% Evaluate both ends of the interval
y1 = feval(f, low);
y2 = feval(f, high);
i = 0; 
% Display error and finish if signs are not different
if y1 * y2 > 0
   disp('Have not found a change in sign. Will not continue...');
   return
end 
% Work with the limits modifying them until you find
% a function close enough to zero.
disp('Iter    low        high          x0');
while (abs(high - low) >= tol)
    i = i + 1;
    % Find a new value to be tested as a root
    m = (high + low)/2;
    y3 = feval(f, m);
    if y3 == 0
        fprintf('Root at x = %f \n\n', m);
        return
    end
    fprintf('%2i \t %f \t %f \t %f \n', i-1, low, high, m);   
    
    x0(i) = m; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

      % Update the limits
      if y1 * y3 > 0
          low = m;
          y1 = y3;
      else
          high = m;
      end
end 

% Show the last approximation considering the tolerance
w = feval(f, m);
fprintf('\n x = %f produces f(x) = %f \n %i iterations\n', m, y3, i-1);
fprintf(' Approximation with tolerance = %f \n', tol);
end