Demonstratie - metoda lui Jacobi
Cuprins
Initializare
Pregatirea matricelor metodei
Prima iteratie
A doua iteratie
Dupa 25 de iteratii
Consideram sistemul
Initializare
A = [2,1;5,7];
b = [4;19];
xn = [2;1];
Pregatirea matricelor metodei
M = diag(diag(A))
M =
2×2
2 0 0 7
N = M -A
N =
2×2
0 -1 -5 0
Prima iteratie
xv = xn;
xn = M\(N*xv+b);
ea = norm(xn-xv,inf);
xn, ea
xn =
2×1
1.500000000000000 1.285714285714286
ea =
0.500000000000000
A doua iteratie
xv = xn;
xn = M\(N*xv+b);
ea = norm(xn-xv,inf);
xn, ea
xn =
2×1
1.357142857142857 1.642857142857143
ea =
0.357142857142857
Dupa 25 de iteratii
for
k=1:23
xv = xn;
xn = M\(N*xv+b);
ea = norm(xn-xv,inf);
end
xn
xn =
2×1
1.000002153146738 1.999996924076088
ea
ea =
2.153146738237410e-06
er =ea/norm(xn,inf)
er =
1.076575024850136e-06