实验一Gauss消元法运行结果.docx
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实验一Gauss消元法运行结果
（1）
>>A=[1-12-1;2-23-3;1110;1-143]
A=
1-12-1
2-23-3
1110
1-143
>>b=[-8;-20;-2;4]
b=
-8
-20
-2
4
>>Gauss（A,b）
ans=
方程的解为：
x=
-6.999999999999995
2.999999999999998
1.999999999999997
2.000000000000002
ans=
将解代回原方程的b值为：
b1=
-8.000000000000000
-20.000000000000000
-1.999999999999999
4.000000000000001
ans=
用Gauss消元法求解的误差为：
eps=
8.881784197001252e-016
（2）
>>A=[2-23-3;0.52-0.51.5;0.502.54.5;0.500.2-0.4]
A=
2.0000-2.00003.0000-3.0000
0.50002.0000-0.50001.5000
0.500002.50004.5000
0.500000.2000-0.4000
>>b=[-14;6;4;4]
b=
-14
6
4
4
>>Gauss（A,b）
ans=
方程的解为：
x=
25.161290322580641
-16.612903225806445
-22.129032258064509
10.387096774193546
ans=
将解代回原方程的b值为：
b1=
-13.999999999999986
6.000000000000005
4.000000000000007
3.999999999999998
ans=
用Gauss消元法求解的误差为：
eps=
1.421085471520200e-014
（3）
当n=10,epa=10^（-8）时
>>Hilbert（10）
ans=
调用Matlab中的求解方法得方程的解为：
X=
1.0e+008*
-0.000010000536808
0.000980145358690
.023*********
0.233041295975382
-1.210849606049417
3.594699761410605
-6.323293521651502
6.511359727102452
-3.623250622643409
0.840659070115685
ans=
将解代回原方程的b值为：
B=
1.000000016763806
2.000000011175871
3.000000013038516
3.999999996274710
4.999999996274710
6.000000011175871
6.999999977648258
8.000000002793968
8.999999997206032
9.999999999068677
ans=
调用Matlab中的求解方法所得解的误差为：
Eps=
2.235174179077148e-008
ans=
用Gauss消元法求解
ans=
方程的解为：
x=
1.0e+008*
-0.000009998189333
0.000979943729515
.023*********
0.233002589297955
-1.210665589649560
3.594195329741595
-6.322467936982889
6.510563619059260
-3.622833473612402
0.840567489802648
ans=
将解代回原方程的b值为：
b1=
1.000000022351742
2.000000010244548
3.000000001862645
3.999999999068677
4.999999997206032
6.000000004656613
7.000000005587935
8.000000001862645
9.000000002793968
9.999999999068677
ans=
用Gauss消元法求解的误差为：
eps=
2.235174179077148e-008
>>Hilbert（20）
ans=
调用Matlab中的求解方法得方程的解为：
Warning:
Matrixisclosetosingularorbadlyscaled.
Resultsmaybeinaccurate.RCOND=1.155429e-019.
>InHilbertat10
X=
1.0e+011*
-0.000000054969082
0.000007449529227
-0.000240144656571
0.003112896556161
-0.018623674273773
.0416********
0.088208328284896
-0.760862576869690
1.891773066130101
-2.216542838697581
1.453213402414779
-2.152********5602
4.065599020002215
-1.550761430815151
-4.686523239294571
5.376685855620782
0.274775676104780
-3.514618861096992
2.109957473539846
-0.403931979506409
ans=
将解代回原方程的b值为：
B=
0.999998807907104
2.000000476837158
3.000002145767212
4.000010490417481
4.999999046325684
6.000000476837158
6.999995708465576
8.000007390975952
8.999995946884155
9.999998331069946
10.999999284744263
12.000000000000000
12.999996185302734
13.999998807907104
14.999997377395630
15.999998331069946
17.000001907348633
18.000001668930054
18.999998569488525
20.000003576278687
ans=
调用Matlab中的求解方法所得解的误差为：
Eps=
1.049041748046875e-005
ans=
用Gauss消元法求解
ans=
方程的解为：
x=
1.0e+011*
-0.000000019403479
0.000002224327321
-0.000052948755227
0.000292943947258
0.003055979360522
-0.048410769637596
0.272233813446375
-0.801741932331504
1.279514828414700
-1.002230604726971
0.512286793235479
-1.217355332825580
1.628287811382938
.0728********
-4.445149808843506
4.240040586321134
-2.062975569006028
.022*********
-0.640594666579924
0.187********8494
ans=
将解代回原方程的b值为：
b1=
1.000001788139343
1.999997138977051
2.999997258186340
3.999997019767761
4.999995827674866
5.999998450279236
7.000000834465027
7.999997615814209
8.999993085861206
10.000001668930054
11.000000953674316
11.999999165534973
12.999999761581421
13.999998450279236
14.999994039535522
15.999999046325684
17.000002145767212
18.000002562999725
18.999998450279236
20.000000059604645
ans=
用Gauss消元法求解的误差为：
eps=
6.914138793945313e-006
>>Hilbert（30）
ans=
调用Matlab中的求解方法得方程的解为：
Warning:
Matrixisclosetosingularorbadlyscaled.
Resultsmaybeinaccurate.RCOND=1.555731e-019.
>InHilbertat10
X=
1.0e+011*
-0.000000050506225
0.000007568762891
-0.000273590815198
0.004101377124596
-0.030792994803548
0.121204285683849
-0.215729534847172
-0.062130184878808
0.992470863529221
-1.883878954967795
2.148045955618994
-2.372296695367503
1.402446326940873
1.804721725821794
-3.173********9335
1.946697147161058
-1.844064345727258
0.543926909827089
0.665044194419229
0.983927606738467
0.492746502337262
-2.282845920928748
0.978098080016813
-2.019282671948588
2.084246999747439
-1.181********7472
2.454810307611026
-0.719091628435689
-1.791390611941243
0.954324727748007
ans=
将解代回原方程的b值为：
B=
0.999999523162842
2.000000953674316
2.999994754791260
4.000003337860107
5.000000476837158
5.999999523162842
6.999997615814209
8.000000476837158
8.999997138977051
10.000000953674316
11.000001907348633
11.999999523162842
12.999998092651367
13.999999046325684
15.000001907348633
15.999999523162842
17.000000715255737
17.999999761581421
19.000000000000000
20.000000953674316
21.000001668930054
22.000000476837158
23.000001907348633
24.000001430511475
25.000000238418579
25.999998807907104
27.000000238418579
28.000000476837158
29.000000000000000
29.999999046325684
ans=
调用Matlab中的求解方法所得解的误差为：
Eps=
5.245208740234375e-006
ans=
用Gauss消元法求解
ans=
方程的解为：
x=
1.0e+011*
-0.000000076924755
0.000010845649319
-0.000357391268467
0.004551869918884
.023*********
0.003581211220936
0.519662030083193
-2.541090281282031
5.709794435130497
-6.689213124309094
4.969593285515742
-6.166********2056
7.479141264972106
-0.018684224926736
-4.649734241188472
-2.515216627191450
4.017514940108231
-1.998991754483997
7.340894880180981
-4.295019884673321
-0.761317470166880
.0744********
2.577440109353636
-1.009537808913537
.0474********
-8.960421090873131
5.484779955047636
-4.493095782856459
2.479166597368471
-0.435927366166195
ans=
将解代回原方程的b值为：
b1=
0.999952316284180
1.999955892562866
2.999987363815308
3.999991655349731
4.999985933303833
5.999999761581421
6.999992132186890
8.000001668930054
9.000001668930054
10.000003814697266
10.999994516372681
12.000005125999451
13.000005364418030
13.999999165534973
14.999996304512024
15.999997377395630
17.000003099441528
18.000004053115845
19.000004053115845
20.000001668930054
20.999999523162842
21.999994039535522
22.999998569488525
23.999999403953552
24.999998211860657
25.999994993209839
26.999999761581421
27.999997854232788
28.999995112419128
30.000000596046448
ans=
用Gauss消元法求解的误差为：
eps=
4.768371582031250e-005
>>
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