Newton methods for solving nonlinear

Please help me fix this code programe

main()

X = 4×1

22.1000 20.0000 5.0000 2.0000

Kết quả:
Nhiệt độ nước lớn nhất là: 22.1

function main()
X0 = [25; 20; 4; 1];
% Áp dụng phương pháp Newton
X = newtons_method(X0)
% Hiển thị kết quả
disp('Kết quả:')
disp(['Nhiệt độ nước lớn nhất là: ', num2str(X(1))]);
end
function F = equations(X)
F = [X(1) - (X(2) + 0.5 * X(3) - 0.2 * X(4));
    X(2) - 20;
    X(3) - 5;
    X(4) - 2];
end
function J = jacobian(X)
J = [1, -0.5, -0.1, 0.2;
    0, 1, 0, 0;
    0, 0, 1, 0;
    0, 0, 0, 1];
end
function X = newtons_method(X0)
% Phương pháp Newton
max_iterations = 100;
tolerance = 1e-6;
X = X0;
for i = 1:max_iterations
    F = equations(X);
    J = jacobian(X);
    delta_X = -J \ F;
    X = X + delta_X;
    if norm(delta_X, inf) < tolerance
        break;
    end
end
end

[Torsten]

Ok, the first row of your Jacobian is wrong and your system of equations is a linear one so that you could have solved it easier than with Newton's method, but the iteration converges. So what exactly is your question ?

[Khai]

This is my lesson: We have a lake and we want to determine its maximum teamperature, the temperature is T, and other affecting factors are the temperature of surrounding environment(Te), the amounts of UV rays(UV), the amounts of nutrients(N). F1(T,Te,UV,N)=T−(Te+0.5*UV−0.2*N) F2(T,Te,UV,N)=Te-20 F3(T,Te,UV,N)=UV-5 F4(T,Te,UV,N)=N-2 T_zero=25, Te_zero=20, UV_zero=4, N_zero=1

[Torsten]

I don't understand your lesson. If F1,...,F4 have to be 0, why are you talking about a "maximum temperature" ? T is uniquely determined by the four equations - there is no degree of freedom to maximize T.

[Khai]

Oh because this lesson is created by myself, therefore it is will not suistable. If you have any ideas, please introduce for me a new one. The only condition is that using the newton method for solving nonlinear to determine the maximum temperature of a source water

[Torsten]

We have enough problems in the world - why inventing a new one ?

[John D'Errico]

Your "solver" works. At least it does on the trivial example problem you chose, which is purely linear, so it will "converge" in one iteration. So where is the problem?

[Khai]

[Khai]

this is my new lesson. Please help me solve it