disp('question 2)a)') //exemples de R. S. Wilson
A=[10 7 8 7 ;
7 5 6 5 ;
8 6 10 9 ;
7 5 9 10 ];
B=[32 23 33 31]';
deltaA=[ 0 0 0.1 0.2 ;
0.08 0.04 0 0 ;
0 -0.02 -0.11 0 ;
-0.01 -0.01 0 -0.02 ];
deltaB=[0.1 -0.1 0.1 -0.1]';
spectreA=spec(A);
printf(' \nLes valeurs propres de A sont :\n..
lambda1 = %.2f, lambda2 = %.2f, lambda3 = %.2f et lambda4 = %.2f\n ',..
spectreA(1),spectreA(2),spectreA(3),spectreA(4))
condA=cond(A)
condAbis=max(abs(spectreA))/min(abs(spectreA))
disp('question 2)b)')
X=A\B
Xbis=A\(B+deltaB)
Xter=(A+deltaA)\B
disp('question 2)c)')
quotient1=norm(Xbis-X)/norm(X)
majorant1=condA*(norm(deltaB)/norm(B))
quotient2=norm(Xter-X)/norm(Xter)
majorant2=condA*(norm(deltaA)/norm(A))