Demonstratie - metoda Gauss-Seidel
Cuprins
Initializare
Pregatirea matricelor metodei
Prima iteratie
A doua iteratie
Dupa 20 de iteratii
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