out.txt

高斯GS与超松弛SOR迭代算法解线性方程组

G-S迭代过程：
          x[0]          x[1]          x[2]

1:               0           -0.5      0.6666667
2:     -0.08333333     -0.2083333      0.8333333
3:       0.1041667       -0.03125       1.013889
4:       0.2378472      0.1258681       1.163194
5:       0.3537326      0.2584635        1.29022
6:       0.4517867      0.3710033       1.397931
7:       0.5349844      0.4664578         1.4893
8:       0.6055539       0.547427       1.566803
9:       0.6654141      0.6161084       1.632544
10:       0.7161901      0.6743669       1.688308
11:       0.7592604      0.7237842        1.73561
12:       0.7957945       0.765702       1.775733
13:       0.8267842      0.8012585       1.809767
14:        0.853071      0.8314191       1.838636
15:       0.8753686      0.8570025       1.863125
16:       0.8942824      0.8787035       1.883896
17:       0.9103259      0.8971112       1.901516
18:       0.9239346      0.9127253       1.916462
19:       0.9354781      0.9259699       1.929139
20:       0.9452698      0.9372045       1.939893
21:       0.9535755      0.9467342       1.949015
22:       0.9606208      0.9548177       1.956752
23:       0.9665969      0.9616745       1.963315
24:       0.9716661      0.9674907       1.968882
25:        0.975966      0.9724242       1.973605
26:       0.9796133       0.976609        1.97761
27:       0.9827071      0.9801588       1.981008
28:       0.9853315      0.9831699        1.98389
29:       0.9875575       0.985724       1.986335
30:       0.9894458      0.9878905       1.988409
31:       0.9910475      0.9897282       1.990168
32:       0.9924061       0.991287        1.99166
33:       0.9935585      0.9926093       1.992926
34:       0.9945361      0.9937309       1.993999
35:       0.9953652      0.9946823        1.99491
36:       0.9960686      0.9954893       1.995682
37:       0.9966652      0.9961738       1.996338
38:       0.9971713      0.9967545       1.996893
39:       0.9976006       0.997247       1.997365
40:       0.9979647      0.9976648       1.997765
41:       0.9982736      0.9980192       1.998104
42:       0.9985356      0.9983198       1.998392
43:       0.9987578      0.9985748       1.998636
44:       0.9989463      0.9987911       1.998843
45:       0.9991062      0.9989745       1.999018
46:       0.9992419      0.9991301       1.999167
47:       0.9993569      0.9992622       1.999294
48:       0.9994545      0.9993741       1.999401
49:       0.9995373      0.9994691       1.999492
50:       0.9996075      0.9995497       1.999569
51:       0.9996671       0.999618       1.999634
52:       0.9997176       0.999676        1.99969
53:       0.9997605      0.9997252       1.999737
54:       0.9997968      0.9997669       1.999777
55:       0.9998276      0.9998022       1.999811
56:       0.9998538      0.9998323       1.999839
57:        0.999876      0.9998577       1.999864
58:       0.9998948      0.9998793       1.999884
59:       0.9999108      0.9998976       1.999902
60:       0.9999243      0.9999132       1.999917
61:       0.9999358      0.9999263       1.999929
62:       0.9999455      0.9999375        1.99994
63:       0.9999538       0.999947       1.999949
64:       0.9999608       0.999955       1.999957
65:       0.9999668      0.9999619       1.999963
66:       0.9999718      0.9999677       1.999969
67:       0.9999761      0.9999726       1.999974
68:       0.9999797      0.9999767       1.999978
69:       0.9999828      0.9999803       1.999981
70:       0.9999854      0.9999833       1.999984
71:       0.9999876      0.9999858       1.999986
72:       0.9999895       0.999988       1.999988
73:       0.9999911      0.9999898        1.99999
74:       0.9999924      0.9999913       1.999992
75:       0.9999936      0.9999926       1.999993
76:       0.9999946      0.9999938       1.999994
77:       0.9999954      0.9999947       1.999995
78:       0.9999961      0.9999955       1.999996
79:       0.9999967      0.9999962       1.999996
80:       0.9999972      0.9999968       1.999997
81:       0.9999976      0.9999973       1.999997
82:        0.999998      0.9999977       1.999998
83:       0.9999983       0.999998       1.999998
84:       0.9999985      0.9999983       1.999998
85:       0.9999988      0.9999986       1.999999
86:        0.999999      0.9999988       1.999999
87:       0.9999991       0.999999       1.999999
88:       0.9999992      0.9999991       1.999999
89:       0.9999994      0.9999993       1.999999
90:       0.9999995      0.9999994       1.999999
91:       0.9999995      0.9999995       1.999999

用G-S迭代法计算方程组的解为:
x[0]=0.9999995
x[1]=0.9999995
x[2]=1.999999
迭代次数:91次
G-S迭代过程的运行时间为0.187秒！
SOR迭代过程：
          x[0]          x[1]          x[2]

1:               0         -0.725      0.7491667
2:      -0.2540521    -0.03979193      0.9516176
3:       0.4304357       0.294895       1.514881
4:       0.5692473      0.6532903       1.674954
5:       0.8246449      0.7932283       1.861637
6:       0.8788436      0.9048954        1.91177
7:       0.9535862      0.9451804       1.964278
8:       0.9681927        0.97571       1.977221
9:       0.9884457      0.9860389        1.99117
10:       0.9918769      0.9939916       1.994239
11:        0.997211      0.9965051       1.997866
12:       0.9979477      0.9985376       1.998555
13:       0.9993394      0.9991313       1.999491
14:       0.9994831      0.9996474       1.999638
15:       0.9998458      0.9997846        1.99988
16:       0.9998697      0.9999155       1.999909
17:       0.9999645      0.9999466       1.999972
18:       0.9999671      0.9999799       1.999977
19:        0.999992      0.9999867       1.999994
20:       0.9999916      0.9999952       1.999994
21:       0.9999982      0.9999967       1.999999
22:       0.9999979      0.9999989       1.999999
23:       0.9999996      0.9999992              2
24:       0.9999995      0.9999997              2
25:       0.9999999      0.9999998              2
26:       0.9999999      0.9999999              2
27:               1      0.9999999              2
28:               1              1              2

用SOR迭代法计算方程组的解为:
x[0]=1
x[1]=1
x[2]=2
迭代次数:28次
SOR迭代过程的运行时间为0.047秒！