function noncon(a, b, x0, epsilon);

% Study the convergence of interval bisection, Newton, Global Newton for
% solving nonlinear equation in 1D. 
% Input: 
%        [a, b]: initial interval for the interval bisection and Global Newton
%           x_0: initial guess for Newton
%       epsilon: convergence tolerence 

% Matlab fzero function
z1 = fzero(inline('exp(2*sin(x)) - x'), -8)
sol = z1; % Exact solution

% Plot the history of interval bisection mathod.
% Give initial interval [a,b], and convergence tolerance
[x_bi, f_bi] = bisec('myfunction', a, b, epsilon);
error_bi = x_bi - sol*ones(1,length(x_bi)); 

% Newton method with different initial guesses 
[x_new, f_new] = Newton('myfunction', x0, epsilon); 
error_new = x_new - sol*ones(1,length(x_new));

[x_Gnew, f_Gnew] = GlobalNewton('myfunction', a, b, epsilon); 
error_Gnew = x_Gnew - sol*ones(1,length(x_Gnew));

semilogy(1:length(error_bi), abs(error_bi), '-*', 1:length(error_new), abs(error_new), '-d', 1:length(error_Gnew), abs(error_Gnew), '-o');
legend('Interval Bisection', 'Standard Newton', 'Global Newton', 3);