function [x_new,k] = bisection(f,xL,xR)
% Computes iterates of the secant method for solving f(x) = 0
% returns iterate where |f(x_k)| < 1e-10 or k=100

% Initialize values
maxsteps = 100;
k = 1;
fL = f(xL);
fR = f(xR);

% Basic error-checking
if (fL*fR > 0)
  error('Endpoints give same sign');
end

% Find new point
x_new = (xL+xR)/2;
f_new = f(x_new);

while ((k < maxsteps) && abs(f_new) > 1e-10)

  % Update endpoints
  if(f_new == 0)
    break
  else if (fL*f_new > 0)
      xL = x_new;
      fL = f_new;
  else
    xR = x_new;
    fR = f_new;
  end
  k = k+1;
    
  % Compute updated point
  x_new = (xL+xR)/2;
  f_new = f(x_new);
end

end