《线性方程组求解》word版.docx

A=1 2 3 4; 4 3 2 1; 1 3 2 4; 4 1 3 2;B=5 1; 4 2; 3 3; 2 4;x=inv(A)*Bnorm(A*x-B) 若为0，则正确x = -1.8000 2.4000 1.8667 -1.2667 3.8667 -3.2667 -2.1333 2.7333ans = 5.2283e-015 xl=inv(sym(A)*Bnorm(double(A*xl-B) 精确解xl = -9/5, 12/5 28/15, -19/15 58/15, -49/15 -32/15, 41/15ans = 0 rank(A)rank(A B) rank(A)=rank(A B)=m有唯一解ans = 4ans = 4 ！方解！ A=1 2 3 4; 2 2 1 1; 2 4 6 8; 4 4 2 2;B=1;3;2;6;C=A B; rank(A), rank(C)Z=null(A,r)x0=pinv(A)*B ans = 2 2Z = 2.0000 3.0000 -2.5000 -3.5000 1.0000 0 0 1.0000x0 = 0.9542 0.7328 -0.0763 -0.2977 al=randn(1); a2=rand(1);x=al*Z(:,1)+a2*Z(:,2)+x0;norm(double(A*x-B) ans = 4.9651e-015 ！解析解！ A=1 2 3 4; 2 2 1 1; 2 4 6 8; 4 4 2 2;B=1;3;2;6;C=A B; rank(A), rank(C)Z=null(sym(A)x0=sym(pinv(A)*B) ans = 2 2Z = 2, 3 -5/2, -7/2 1, 0 0, 1x0 = 125/131 96/131 -10/131 -39/131 al=randn(1); a2=rand(1);x=al*Z(:,1)+a2*Z(:,2)+x0;norm(double(A*x-B) ans = 0 A=1 2 3 4; 2 2 1 1; 2 4 6 8; 4 4 2 2; B=1:4;C=A B;rank(A), rank(C) x=pinv(A)*Bnorm(A*x-B) ans = 2 3x = 0.5466 0.4550 0.0443 -0.0473ans = 0.4472 clear A=1 2 3;4 5 6; 7 8 0;C=-10, 5, 4; 5, 6, 7; 4, 7, 9;X=lyap (A, C)norm(A*X+X*A +C) X = -3.9444 3.8889 0.3889 3.8889 -2.7778 0.2222 0.3889 0.2222 -0.1111ans = 2.4390e-014 A=1 2 3;4 5 6; 7 8 0;C=-10, 5, 4; 5, 6, 7; 4, 7, 9;A0=sym(kron(A,eye(3)+kron(eye(3),A);c=reshape(C,9,1);x0=-inv(A0)*c;x=reshape(x0,3,3)norm(double(A*x+x*A+C) x = -71/18, 35/9, 7/18 35/9, -25/9, 2/9 7/18, 2/9, -1/9ans = 0 A=-2 1 0;0 -2 1;0 0 -2,zeros(3,2);zeros(2,3),-5 1;0 -5expm(A)logm(ans)norm(ans-A) A = -2 1 0 0 0 0 -2 1 0 0 0 0 -2 0 0 0 0 0 -5 1 0 0 0 0 -5ans = 0.1353 0.1353 0.0677 0 0 0 0.1353 0.1353 0 0 0 0 0.1353 0 0 0 0 0 0.0067 0.0067 0 0 0 0 0.0067ans = -2.0000 1.0000 -0.0000 0 0 0