Metoda potęgowa
A=[12 2 5 4;2 9 2 4;3 5 15 1;2 3 1 10]y=[1;2;3;4]blad=0.0001iter=0;while iter <= 10iter=iter+1y=y/norm(y)%wektor znormalizowanyx=A*y;l=y'*xy=x end
Metoda Gerszgorina
clcclearA=[ 12 8 5 -4; 1 8 6 4; 1 2 4 3; 1 2 3 2]D=diag(A)r=zeros(4,1);r(1)=abs(A(1,2))+abs(A(1,3))+abs(A(1,4))r(2)=abs(A(2,1))+abs(A(2,3))+abs(A(2,4))r(3)=abs(A(3,1))+abs(A(3,2))+abs(A(3,4))r(4)=abs(A(4,1))+abs(A(4,2))+abs(A(4,3))C=[r(1);r(2);r(3);r(4)]E=D-CF=D+Cmin=min(E)max=max(F)t=linspace(0, 2*pi, 200);% okrąg o środku (a,b) i promieniu r we wsp. biegunowychfor i=1:4x=A(i,i)+r(i)*cos(t);y=r(i)*sin(t);plot(x,y);axis equal;hold on;end% osie układuplot([-2*r 2*r], [0 0],'k:');plot([0 0], [-2*r 2*r],'k:');for i=1:4% środek okręgu - czerwona kropkaplot(A(i,i),0,'.','MarkerSize',14,'MarkerEdge','r');hold on;endhold off;
Metoda Gaussa
clcA=[12 2 7 4; 2 9 2 8; 3 5 15 9; 7 3 5 10]B=[10 2 4 13]';C=[A,B];a=det(A);if a==0;disp('zla macierz');stopend%zerowanie pierwszej kolumnyC(2,:)=C(2,:)-C(1,:)*(C(2,1)/A(1,1))C(3,:)=C(3,:)-C(1,:)*(C(3,1)/A(1,1))C(4,:)=C(4,:)-C(1,:)*(C(4,1)/A(1,1))%zerowanie drugiej kolumnyC(3,:)=C(3,:)-C(2,:)*(C(3,2)/C(2,2))C(4,:)=C(4,:)-C(2,:)*(C(4,2)/C(2,2))%zerowanie 3ciej kolumnyC(4,:)=C(4,:)-C(3,:)*(C(4,3)/C(3,3))%backsubq=C(4,5)/A(4,4)w=1/C(3,3)*(C(3,5)-C(3,4)*q)e=1/C(2,2)*(C(2,5)-C(2,4)*q-C(2,3)*w)r=1/C(1,1)*(C(1,5)-C(1,4)*q-C(1,3)*w-C(1,2)*e)
Metoda Gaussa-Seidla
A=[11 3 4 1; 5 14 5 3; 1 7 16 2; 2 6 3 17]B=[3; 5; 3; 1]x=[0; 0; 0; 0];tol=10^(-6);i=0;whilei=i+1y=xfor i=1:4x(i)=x(i)+(B(1,1)-A(i,:)*x)/A(i,i);endend
m_i_c_h_a_l