用共軛梯度法解方程,用Jacobi方法求矩陣的全部特征值和特征向量

用共軛梯度法解方程，用Jacobi方法求矩陣的全部特征值和特征向量二、代碼clear%輸入矩陣階數(shù)n=input('矩陣階數(shù)n=');A=zeros(n,n);b=zeros(n,1);fori=1:n/2b(2*i-1,1)=5;b(2*i,1)=6;endfori=2:n-1A(i,i)=4;A(i,i-1)=1;A(i,i+1)=1;endA(1,1)=4;A(n,n)=4;A(n,n-1)=1;X=zeros(n,1);fori=1:nX(i,1)=1;end%用共軛梯度法求解方程fprintf('方程的精確解\n');Xfprintf('用共軛法求解方程\n');x=cg(A,b)%用方法求解方程的特征值和特征向量fprintf('用Jacobi方法求解方程的特征值和特征向量\n');[D,V]=tezhengJaco(A)三、數(shù)值結(jié)果baogaoer矩陣階數(shù)n=10方程精確解X=1111111111用共軛梯度法求解方程k=100x=1.25001.01040.70851.15550.66941.16680.66341.17940.61881.3453用方法Jacobi求解矩陣的全部特征值及特征向量D=Columns1through74.00000000000.13825.90210.00000.0000-0.00000.00000.0000-0.26290.00005.61800.00000.0000-0.0000-0.0000-0.36180.00000.00005.1756-0.00000-0.0000-0.4253-0.0000-0.0000-0.00004.6180-0.0000-0.00000.4472-0.00000.00000.0000-0.00004.0000-0.0000-0.4253-0.0000-0.00000.0000-0.0000-0.00003.38200.3618-0.0000-0.0000-0.00000.00000.00000.00000.26290.0000-0.00000.0000-0.00000.00000.00000.13820.0000-0.00000.00000.00000.0000-0.0000Columns8through100000-0.0000-0.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.0000-0.00002.8244-0.00000.00000.00002.3820-0.0000-0.0000-0.00002.0979V=Columns1through71.00000000000.1382-0.2629-0.3618-0.42530.4472-0.425300.2629-0.4253-0.4253-0.2629-0.00000.262900.3618-0.4253-0.13820.2629-0.44720.262900.4253-0.26290.26290.4253-0.0000-0.425300.44720.00000.44720.00000.44720.000000.42530.26290.2629-0.42530.00000.425300.36180.4253-0.1382-0.2629-0.4472-0.262900.26290.4253-0.42530.2629-0.0000-0.262900.13820.2629-0.36180.42530.44720.4253Columns8through100000.36180.26290.1382-0.4253-0.4253-0.26290.13820.42530.36180.2629-0.2629-0.4253-0.44720.00000.44720.26290.2629-0.42530.1382-0.42530.3618-0.42530.4253-0.26290.3618-0.26290.1382>baogaoer矩陣階數(shù)n=20方程精確解X=11111111111111111111用共軛梯度法求解方程k=76x=1.25001.01040.70851.15540.66971.16590.66691.16660.66671.16670.66671.16670.66661.16670.66641.16760.66321.17950.61881.3453用方法Jacobi求解矩陣的全部特征值及特征向量D=Columns1through74.00000000000.04955.97540.00000.00000.00000.0000-0.0000-0.0977-0.00005.9021-0.00000.00000.00000.0000-0.1436-0.00000.00005.78200.0000-0.0000-0.0000-0.1859-0.00000.00000.00005.6180-0.0000-0.0000-0.22360.0000-0.00000.00000.00005.41420.0000-0.25580.0000-0.00000.00000.00000.00005.17560.2818-0.0000-0.00000.00000.00000.0000-0.00000.30080.00000.00000.00000.0000-0.0000-0.00000.3123-0.0000-0.00000.0000-0.00000.0000-0.00000.3162-0.0000-0.0000-0.00000.00000.0000-0.0000-0.3123-0.0000-0.0000-0.00000.0000-0.00000.0000-0.3008-0.0000-0.00000.0000-0.0000-0.0000-0.00000.2818-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.2558-0.0000-0.0000-0.0000-0.00000.00000.00000.22360.00000.00000.0000-0.0000-0.00000.00000.1859-0.0000-0.0000-0.0000-0.00000.0000-0.00000.1436-0.0000-0.0000-0.00000.0000-0.00000.0000-0.09770.00000.0000-0.00000.0000-0.00000.00000.04950.0000-0.00000.00000.00000.00000.0000Columns8through140000000-0.0000-0.0000-0.00000.00000.00000-0.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.0000-0.00000-0.0000-0.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.00000.0000-0.0000-0.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.0000-0.00000.00000.00000.00004.90800-0.00000.0000-0.00000.0000-0.00000.00004.6180-0.0000-0.0000-0.00000.0000-0.00000.0000-0.00004.31290.0000-0.0000-0.00000.00000.0000-0.0000-0.00004.00000.00000.0000-0.00000.00000.00000.00000.00003.6871-0.00000.00000.00000.00000.00000.00000.00003.38200.0000-0.0000-0.0000-0.00000.0000-0.00000.00003.09200.0000-0.00000.00000.0000-0.00000.00000.00000.0000-0.00000.00000.00000.00000.0000-0.0000-0.00000.00000.0000-0.00000.00000.0000-0.00000.00000.00000.0000-0.00000.00000.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.0000Columns15through20000000-0.00000.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.00000.0000-0.00000.00000.00000.00000.00000.0000-0.00000.00000.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.00000.00000.0000-0.0000-0.00000.00000.00000.00000.00000.0000-0.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.00000.0000-0.00000.0000-0.00002.8244-0.0000-0.00000.0000-0.0000-0.00000.00002.58580.00000.0000-0.0000-0.00000.00000.00002.38200.0000-0.0000-0.00000.0000-0.0000-0.00002.21800.00000.0000-0.00000.00000.0000-0.00002.09790.00000.0000-0.00000.0000-0.00000.00002.0246V=Columns1through71.000000000000.0495-0.0977-0.1436-0.1859-0.2236-0.255800.0977-0.1859-0.2558-0.3008-0.3162-0.300800.1436-0.2558-0.3123-0.3008-0.2236-0.097700.1859-0.3008-0.3008-0.1859-0.00000.185900.2236-0.3162-0.2236-0.00000.22360.316200.2558-0.3008-0.09770.18590.31620.185900.2818-0.25580.04950.30080.2236-0.097700.3008-0.18590.18590.30080.0000-0.300800.3123-0.09770.28180.1859-0.2236-0.255800.3162-0.00000.31620.0000-0.3162-0.000000.31230.09770.2818-0.1859-0.22360.255800.30080.18590.1859-0.3008-0.00000.300800.28180.25580.0495-0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