PPAGAF NR

UNULIOYLOI

clc
% NEWTON RAPHSON
syms x1
syms x2
syms x3
f1 = 3*x1 - cos(x2*x3) - 0.5;
f2 = x1*x1 - 81*(x2 + 0.1)^2 + sin(x3) + 1.06;
f3 = exp(x1*x2) + 20*x3 + (10*pi - 3)/3;
% Jacobian Matrix
Df = jacobian([f1; f2; f3], [x1, x2, x3]);
% Initial guess
Xr = [0.11, 0.5, -0.123]';
tolerance = 1e-6; % Tolerance level for convergence
maxIterations = 100; % Maximum number of iterations
% Arrays to store values for plotting
x1_values = [];
x2_values = [];
x3_values = [];
% Iterations
iteration = 0;
error = inf;
while error > tolerance
    F = double(subs([f1; f2; f3], [x1, x2, x3], Xr'));
    J = double(subs(Df, [x1, x2, x3], Xr'));
    deltaX = -J\F;
    XrNew = Xr + deltaX;
    error = norm(XrNew - Xr);
    Xr = XrNew;
    iteration = iteration + 1;
    
    % Store values for plotting
    x1_values(iteration) = Xr(1);
    x2_values(iteration) = Xr(2);
    x3_values(iteration) = Xr(3);
end
% Plotting
iterations = 1:iteration;
figure;
subplot(3, 1, 1);
plot(iterations, x1_values, 'r-');
xlabel('Iteration');
ylabel('x1 Value');
title('Iterations vs x1 Values');
grid on;
subplot(3, 1, 2);
plot(iterations, x2_values, 'g-');
xlabel('Iteration');
ylabel('x2 Value');
title('Iterations vs x2 Values');
grid on;
subplot(3, 1, 3);
plot(iterations, x3_values, 'b-');
xlabel('Iteration');
ylabel('x3 Value');
title('Iterations vs x3 Values');
grid on;