《線性方程組求解》word版

1、.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=invA*BnormA*x-B 假設為0，那么正確x = -1.8000 2.4000 1.8667 -1.2667 3.8667 -3.2667 -2.1333 2.7333ans = 5.2283e-015 xl=invsymA*BnormdoubleA*xl-B 準確解xl = -9/5, 12/5 28/15, -19/15 58/15, -49/15 -32/15, 41/15ans = 0 rankArankA B rankA=rankA B=m有唯一解ans

2、= 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; rankA, rankCZ=nullA,'r'x0=pinvA*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=randn1; a2=rand1;x=al*Z:,1+a2*Z:,2+x0;normdoubleA*x-B ans = 4.9651e-015 ！解析解！ A=1 2 3 4; 2

3、 2 1 1; 2 4 6 8; 4 4 2 2;B=1;3;2;6;C=A B; rankA, rankCZ=nullsymAx0=sympinvA*B ans = 2 2Z = 2, 3 -5/2, -7/2 1, 0 0, 1x0 = 125/131 96/131 -10/131 -39/131 al=randn1; a2=rand1;x=al*Z:,1+a2*Z:,2+x0;normdoubleA*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;rankA, rankC x=pinvA*BnormA*x

4、-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, CnormA*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=symkronA,eye3+

5、kroneye3,A;c=reshapeC',9,1;x0=-invA0*c;x=reshapex0,3,3'normdoubleA*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,zeros3,2;zeros2,3,-5 1;0 -5expmAlogmansnormans-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 -2.00