Demonstratie - metoda Gauss-Seidel

Cuprins
Consideram sistemul

Initializare

A = [2,1;5,7];
b = [4;19];
xn = [2;1];

Pregatirea matricelor metodei

M = tril(A)
M = 2×2
2 0 5 7
N = M -A
N = 2×2
0 -1 0 0

Prima iteratie

xv = xn;
xn = M\(N*xv+b);
ea = norm(xn-xv,inf);
xn, ea
xn = 2×1
1.500000000000000 1.642857142857143
ea = 0.642857142857143

A doua iteratie

xv = xn;
xn = M\(N*xv+b);
ea = norm(xn-xv,inf);
xn, ea
xn = 2×1
1.178571428571429 1.872448979591837
ea = 0.321428571428571

Dupa 20 de iteratii

for k=1:19
xv = xn;
xn = M\(N*xv+b);
ea = norm(xn-xv,inf);
end
xn
xn = 2×1
1.000000000569914 1.999999999592918
ea
ea = 1.025845408619830e-09
er =ea/norm(xn,inf)
er = 5.129227044143157e-10