cavallo

function [x] = RisolviTriangSup(U, y)
% Risolve il sistema triangolare superiore Ux = y

n = length(y);
x(n) = y(n) / U(n, n);

for k = n-1 : -1 : 1
    x(k) = (y(k) - U(k, k+1:n)*x(k+1:n)') / U(k, k);
end

end




function [x] = Gauss(A, b)
% Metodo di eliminazione di Gauss

n = length(b);

for k = 1 : n-1

    for i = k+1 : n
        m(i) = A(i,k) / A(k,k);

        for j = k+1 : n
            A(i,j) = A(i,j) - m(i)*A(k,j);
        end

        b(i) = b(i) - m(i)*b(k);
    end
end

x = RisolviTriangSup(triu(A), b);
end





A = [   -2.3    4   -1.5    -1;
        4       -9.2 0.9    5;
        -4      5    -5     5.2;
        -8      8    -13.4  20];

b = [1 -3 3 -2]';

x = Gauss(A, b);
x_true = A\b;

norm(b - A*x') / norm(b)

norm(x_true - x) / norm(x_true)