% Define the function g(x)
g = @(x) x^2 - 2;  % Example function (you can replace this with your function)
 
% Set initial guess
x0 = 1;  % Example initial guess (you can change this)
 
% Set tolerance and maximum number of iterations
tol = 1e-6; 
max_iter = 1000; 
 
% Initialize variables
x_prev = x0;
iterates = zeros(max_iter, 1); % To store the iterates
 
% Fixed-point iteration
for k = 1:max_iter
    x_new = g(x_prev); % Update to the new value
    iterates(k) = x_new; % Store the iterate
 
    % Check for convergence
    if abs(x_new - x_prev) < tol
        fprintf('Converged to %.6f after %d iterations.\n', x_new, k);
        break;
    end
 
    % Update previous iterate
    x_prev = x_new;
end
 
% If the loop completes without convergence
if k == max_iter
    fprintf('Did not converge after %d iterations.\n', max_iter);
end
 
% Plot the iterates to visualize convergence
figure;
plot(1:k, iterates(1:k), '-o');
xlabel('Iteration');
ylabel('Value of x');
title('Fixed Point Iteration');
grid on;
 

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