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

1、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); for i=1:n/2b(2*i-1,1)=5; b(2*i,1)=6; end for i=2:n-1A(i,i)=4;A(i,i-1)=1;A(i,i+1)=1; end A(1,1)=4; A(n,n)=4; A(n,n-1)=1; X=zeros(n,1); for i=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

2、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 =Columns 1 through 74.000000 00000.13825.90210.00000.

3、0000-0.00000.00000.0000-0.26290.00005.61800.00000.0000-0.0000-0.0000-0.36180.00000.00005.1756-0.00000 -0.0000-0.4253-0.0000-0.0000-0.00004.6180-0.0000-0.00000.4472-0.00000.00000.0000-0.00004.0000-0.0000-0.4253-0.0000-0.00000.0000-0.0000-0.00003.38200.3618-0.0000-0.0000-0.00000.00000.00000.00000.2629

4、0.0000-0.00000.0000-0.00000.00000.00000.13820.0000-0.00000.00000.00000.0000-0.0000Columns 8 through 100 0 00 -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 =Columns 1 throu

5、gh 71.00000 0 0000 0.1382-0.2629-0.3618-0.42530.4472-0.42530 0.2629-0.4253-0.4253-0.2629-0.00000.26290 0.3618-0.4253-0.13820.2629-0.44720.26290 0.4253-0.26290.26290.4253-0.0000-0.42530 0.44720.00000.44720.00000.44720.00000 0.42530.26290.2629-0.42530.00000.42530 0.36180.4253-0.1382-0.2629-0.4472-0.26

6、290 0.26290.4253-0.42530.2629-0.0000-0.26290 0.13820.2629-0.36180.42530.44720.4253Columns 8 through 1000 00.36180.26290.1382-0.4253-0.4253-0.26290.13820.42530.36180.2629-0.2629-0.4253-0.44720.00000.44720.26290.2629-0.42530.1382-0.42530.3618-0.42530.4253-0.26290.3618-0.26290.1382 baogaoer 矩陣階數(shù) n=20 方

7、程精確解X =111111111111111111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 =Columns 1 through 74.0000000 0000.04955.97540.00000.00000.00000.0000-0.0000-0.0977-0.00005.9021-0.00000.00

8、000.00000.0000-0.1436-0.00000.00005.78200.0000-0.0000-0.0000-0.1859-0.00000.00000.00005.6180-0.0000-0.0000-0.22360.0000-0.00000.00000.00005.41420.0000-0.25580.0000-0.00000.00000.00000.00005.17560.2818-0.0000-0.00000.00000.00000.0000-0.00000.30080.00000.00000.00000.0000-0.0000-0.00000.3123-0.0000-0.0

9、0000.0000-0.00000.0000-0.00000.3162-0.0000-0.0000-0.00000.00000.0000-0.0000-0.3123-0.0000-0.0000-0.00000.0000-0.00000.0000-0.3008-0.0000-0.00000.0000-0.0000-0.0000-0.00000.2818-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.2558-0.0000-0.0000-0.0000-0.00000.00000.00000.22360.00000.00000.0000-0.0000-0.00

10、000.00000.1859-0.0000-0.0000-0.0000-0.00000.0000-0.00000.1436-0.0000-0.0000-0.00000.0000-0.00000.0000-0.09770.00000.0000-0.00000.0000-0.00000.00000.04950.0000-0.00000.00000.00000.00000.0000Columns 8 through 14000 000 0-0.0000-0.0000-0.00000.00000.00000 -0.0000-0.00000.00000.0000-0.00000.0000-0.0000-

11、0.0000-0.0000-0.0000-0.00000 -0.0000 -0.0000 0.00000.0000-0.0000-0.00000.00000.00000.0000-0.00000.0000-0.0000-0.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.0000-0.00000.00000.00000.00004.90800 -0.0000 0.0000 -0.0000 0.0000 -0.00000.00004.6180-0.0000-0.0000-0.00000.0000-0.00000.0000-0.00004.31290.0

12、000-0.0000-0.00000.00000.0000-0.0000-0.00004.00000.00000.0000-0.00000.00000.00000.00000.00003.6871-0.00000.00000.00000.00000.00000.00000.00003.38200.0000-0.0000-0.0000-0.00000.0000-0.00000.00003.09200.0000-0.00000.00000.0000-0.00000.00000.00000.0000-0.00000.00000.00000.00000.0000-0.0000-0.00000.0000

13、0.0000-0.00000.00000.0000-0.00000.00000.00000.0000-0.00000.00000.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.0000Columns 15 through 20000 000-0.00000.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.00000.0000-0.0000-0.0000

14、-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

15、.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.00000.0000-0.00000.0000-0.00002.8244-0.0000-0.00000.0000-0.0000-0.00000.00002.58580.00000.0000-0.0000-0.00000.00000.00002.38200.0000-0.0000-0.00000.0000-0.0000-0.00002.21800.00000.0000-0.00000.00000.0000-0.00002.09790.00000.000

16、0-0.00000.0000-0.00000.00002.0246Columns 1 through 71.00000000 0000.0495-0.0977-0.1436-0.1859-0.2236-0.255800.0977-0.1859-0.2558-0.3008-0.3162-0.300800.1436-0.2558-0.3123-0.3008-0.2236-0.097700.1859-0.3008-0.3008-0.1859-0.00000.185900.2236-0.3162-0.2236-0.00000.22360.316200.2558-0.3008-0.09770.18590

17、.31620.185900.2818-0.25580.04950.30080.2236-0.097700.3008-0.18590.18590.30080.0000-0.300800.3123-0.09770.28180.1859-0.2236-0.255800.3162-0.00000.31620.0000-0.3162-0.000000.31230.09770.2818-0.1859-0.22360.255800.30080.18590.1859-0.3008-0.00000.300800.28180.25580.0495-0.30080.22360.097700.25580.3008-0

18、.0977-0.18590.3162-0.185900.22360.3162-0.2236-0.00000.2236-0.316200.18590.3008-0.30080.18590.0000-0.185900.14360.2558-0.31230.3008-0.22360.097700.09770.1859-0.25580.3008-0.31620.300800.04950.0977-0.14360.1859-0.22360.2558Columns 8 through 140000 0000.28180.30080.31230.3162-0.3123-0.30080.28180.25580

19、.18590.09770.00000.09770.1859-0.2558-0.0495-0.1859-0.2818-0.31620.28180.1859-0.0495-0.3008-0.3008-0.1859-0.0000-0.1859-0.30080.3008-0.2236-0.00000.22360.3162-0.22360.0000-0.22360.09770.30080.25580.00000.25580.3008-0.09770.31230.1859-0.1436-0.31620.1436-0.18590.31230.1859-0.1859-0.3008-0.0000-0.3008-

20、0.1859-0.1859-0.1436-0.30080.04950.3162-0.04950.3008-0.1436-0.3162-0.00000.31620.00000.31620.00000.3162-0.14360.30080.0495-0.3162-0.0495-0.3008-0.14360.18590.1859-0.3008-0.0000-0.30080.1859-0.18590.3123-0.1859-0.14360.31620.14360.18590.31230.0977-0.30080.25580.00000.2558-0.3008-0.0977-0.2236-0.00000

21、.2236-0.3162-0.22360.0000-0.2236-0.30080.3008-0.1859-0.0000-0.18590.30080.3008-0.04950.1859-0.28180.31620.2818-0.1859-0.04950.2558-0.18590.09770.00000.0977-0.1859-0.25580.2818-0.30080.3123-0.3162-0.31230.30080.2818Columns 15 through 20000 000-0.25580.22360.18590.1436-0.09770.04950.3008-0.3162-0.3008

22、-0.25580.1859-0.0977-0.09770.22360.30080.3123-0.25580.1436-0.1859-0.0000-0.1859-0.30080.3008-0.18590.3162-0.22360.00000.2236-0.31620.2236-0.18590.31620.1859-0.09770.3008-0.2558-0.0977-0.2236-0.3008-0.0495-0.25580.28180.30080.00000.30080.18590.1859-0.3008-0.25580.2236-0.1859-0.2818-0.09770.31230.0000

23、-0.31620.00000.31620.0000-0.31620.25580.22360.1859-0.28180.09770.3123-0.3008-0.0000-0.30080.1859-0.1859-0.30080.0977-0.22360.3008-0.04950.25580.28180.18590.3162-0.1859-0.0977-0.3008-0.2558-0.3162-0.22360.00000.22360.31620.22360.18590.00000.1859-0.3008-0.3008-0.18590.09770.2236-0.30080.31230.25580.14

24、36-0.3008-0.31620.3008-0.2558-0.1859-0.09770.25580.2236-0.18590.14360.09770.0495 baogaoer 矩陣階數(shù) n=30 方程精確解 X =11111111111111111111111111 用共軛梯度法求解方程 k =74x =1.25001.01040.70851.15540.66971.16590.66691.16660.66671.16670.66671.16670.66671.16670.66671.16670.66671.16670.66671.16670.66671.16670.66661.16670

25、.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 =Columns 1 through 74.0000000 0000.02705.9890-0.00000.00000.00000.00000.00000.05370.00005.9563-0.0000-0.0000-0.000000.0798-0.0000-0.00005.9021-0.00000.0000-0.00000.10500.0000-0.00000.00005.8271-0.00000.00000.12910.0000-0.00000.00000.000

26、05.73210.00000.1518-0.00000.0000-0.00000.00000.00005.61800.17280.00000.00000.0000-0.0000-0.00000.00000.1919-0.0000-0.0000-0.0000-0.00000.0000-0.0000-0.2089-0.0000-0.0000-0.00000.00000.00000.0000-0.22360.0000-0.00000.00000.0000-0.00000.00000.2359-0.00000.0000-0.00000.00000.0000-0.00000.24560.0000-0.0

27、0000.00000.0000-0.00000.0000-0.25260.00000.0000-0.0000-0.00000.0000-0.00000.25680.0000-0.00000.0000-0.0000-0.0000-0.00000.25820.00000.0000-0.00000.0000-0.00000.00000.2568-0.0000-0.00000.0000-0.00000.0000-0.00000.2526-0.0000-0.00000.00000.0000-0.00000.00000.24560.00000.00000.00000.00000.00000.00000.2

28、359-0.0000-0.0000-0.00000.00000.0000-0.00000.22360.00000.00000.0000-0.0000-0.00000.00000.20890.0000-0.00000.00000.00000.0000-0.00000.19190.0000-0.00000.00000.00000.00000.00000.17280.0000-0.0000-0.00000.00000.00000.00000.15180.00000.0000-0.0000-0.00000.00000.00000.1291-0.0000-0.0000-0.00000.00000.000

29、0-0.0000-0.10500.0000-0.0000-0.0000-0.00000.0000-0.0000-0.07980.00000.0000-0.00000.0000-0.00000.00000.05370.0000-0.0000-0.0000-0.0000-0.0000-0.00000.02700.00000.0000-0.00000.0000-0.0000-0.0000Columns 8 through 14000 000 0-0.00000.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.00000.0000-0.00000.00000

30、.00000.0000-0.00000.00000.0000-0.00000.00000.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00005.4863-0.0000-0.0000-0.00000.0000-0.0000-0.00000.00005.33830.00000.00000.00000.00000.0000-0.0000-0.00005.17560.0000

31、0.0000-0.0000-0.00000.0000-0.00000.00005.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.00004.8135-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.00004.6180-0.00000.00000.00000.00000.00000.0000-0.00004.41580.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.00000.00000.0000

32、-0.00000.00000.00000.0000-0.0000-0.00000.0000-0.00000.00000.0000-0.00000.00000.0000-0.0000-0.00000.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.00000.0000-0.0000-0.00000.00000.00000.0000-0.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00000.

33、0000-0.00000.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.00000.0000-0.00000.0000-0.0000-0.00000.00000.0000-0.0000-0.00000.0000-0.0000-0.00000.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.

34、0000-0.00000.0000-0.0000-0.0000Columns 15 through 21000 000 0-0.0000-0.0000-0.00000.00000.0000-0.0000-0.00000.00000.00000.00000.00000.0000-0.00000.00000 0.0000 -0.0000 0.0000 0.0000 0.0000 0.00000.00000.0000-0.0000-0.00000.00000.0000-0.00000.0000-0.00000.00000.0000-0.0000-0.00000.00000.0000-0.0000-0

35、.0000-0.0000-0.0000-0.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.00000.00000.0000-0.0000-0.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.0000-0.00000.0000-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.00000.00000.0000-0.00000.00000.00000.

36、00000.00000.00000.0000-0.00000.00000.00000.00000.00004.2091-0.00000.00000.0000-0.0000-0.00000.0000-0.00004.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.00003.79090.00000.0000-0.00000.0000-0.00000.00000.00003.5842-0.0000-0.0000-0.0000-0.00000.00000.0000-0.00003.38200.00000.00000.0000-0.0000-0.0000-

37、0.00000.00003.18650-0.00000.00000.0000-0.00000.00000.00003.00000.0000-0.00000.00000.00000.00000.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.000

38、00.0000-0.00000.00000.00000.00000.00000.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.00000.0000-0.0000-0.00000.00000.0000-0.0000-0.0000Columns 22 through 28000 000 0-0.0000-0.0000-0.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-

39、0.0000-0.00000.0000-0.0000-0.00000.0000-0.0000-0.00000.00000.00000.00000.0000-0.0000-0.0000-0.0000-0.00000.0000-0.00000.00000.0000-0.0000-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00

40、000.0000-0.00000.0000-0.00000 -0.0000 0.0000 -0.0000 0.0000 -0.00000.00000.00000 0.0000 -0.0000 -0.0000 -0.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.00000.0000-0.0000-0.00000.00000.0000-0.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00

41、000.00000.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.00000.0000-0.00000.00000.00000.0000-0.0000-0.00000.0000-0.00000.0000-0.0000-0.00000.00000.00000.00000.0000-0.00000.00000.00000.0000-0.00002.82440.00000.0000-0.0000-0.0000-0.0000-0.00000.00002.66170.00000.00000.00000.0000-0.0

42、000-0.0000-0.00002.51370.0000-0.0000-0.00000.0000-0.0000-0.0000-0.00002.3820-0.0000-0.00000.0000-0.00000.0000-0.0000-0.00002.26790.00000.00000.00000.0000-0.00000.00000.00002.1729-0.00000.00000.0000-0.00000.00000.00000.00002.0979-0.00000.00000.0000-0.00000.00000.0000-0.0000-0.0000-0.0000-0.00000.0000

43、0.0000-0.0000-0.0000Columns 29 through 30000.0000 0.00000.0000 0.0000-0.00000.00000.00000.0000-0.00000.00000.0000-0.00000.00000.00000.0000-0.0000-0.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.00000.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.00000.00000.0000-0.0000-0.00000.0000-0.0

44、0000.00000.0000-0.0000-0.0000-0.0000-0.0000-0.00000.00000.00000.0000-0.0000-0.0000-0.00000.00002.0437-0.0000-0.00002.0110Columns 1 through 71.00000000 0000.0270-0.05370.07980.10500.12910.151800.0537-0.10500.15180.19190.22360.245600.0798-0.15180.20890.24560.25820.245600.1050-0.19190.24560.25680.22360

45、.151800.1291-0.22360.25820.22360.1291-0.000000.1518-0.24560.24560.15180.0000-0.151800.1728-0.25680.20890.0537-0.1291-0.245600.1919-0.25680.1518-0.0537-0.2236-0.245600.2089-0.24560.0798-0.1518-0.2582-0.151800.2236-0.2236-0.0000-0.2236-0.22360.000000.2359-0.1919-0.0798-0.2568-0.12910.151800.2456-0.1518-0.1518-0.2456-0.00