you bisection in matlab

main.m
function root = bisection(f, a, b, tol)
  % f: the function for which we want to find the root
  % a, b: the initial interval [a, b]
  % tol: the tolerance or the desired accuracy
  
  % Check if f(a) and f(b) have opposite signs
  if (sign(f(a)) * sign(f(b))) >= 0
    error('f(a) and f(b) must have opposite signs');
  end
  
  % Bisection iteration
  while (b - a) > tol
    c = (a + b) / 2;
    
    % Check if c is already a root
    if f(c) == 0
      break;
    end
    
    % Update the interval based on the sign of f(c)
    if (sign(f(c)) * sign(f(a))) < 0
      b = c;
    else
      a = c;
    end
  end
  
  % Return the root
  root = (a + b) / 2;
end
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main.m
% Define the function
f = @(x) x^3 - 2*x - 5;

% Call the bisection function
root = bisection(f, 2, 3, 1e-6);

% Display the result
disp(root);
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