实验5线性代数方程组的数值解法Word格式文档下载.docx
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,k+1）+f2;
A1=3.*eye（20,20）;
A2=sparse（1:
19,2:
20,-1/2,20,20）;
A3=sparse（1:
18,3:
20,-1/4,20,20）;
AA=A1+A2+A3+A2'
+A3'
;
A=full（AA）;
b=ones（20,1）;
%输入自选右端项向量b
x0=ones（20,1）;
%输入自选初始向量x0
m=1e-5;
x1=Jacob（x0,A,b,m）;
x2=Gauss（x0,A,b,m）;
结果输出数据：
k
1
2
3
4
5
6
7
x各分量
0.583333
0.527778
0.499421
0.489583
0.485139
0.483239
0.482374
0.75
0.638889
0.602431
0.586034
0.579162
0.576046
0.574639
0.833333
0.715278
0.670139
0.649595
0.640545
0.636396
0.634487
0.743056
0.693287
0.671586
0.661185
0.6564
0.654137
0.704282
0.681713
0.670915
0.665718
0.663238
0.707755
0.685571
0.674716
0.669367
0.666768
0.708333
0.687066
0.676272
0.670924
0.668274
0.687452
0.67685
0.671535
0.668883
0.6875
0.677039
0.671767
0.669127
0.677079
0.671844
0.66921
8
9
10
11
12
13
14
15
x各分量值
0.48198
0.481798
0.481713
0.481672
0.481653
0.481644
0.48164
0.481638
0.573988
0.573686
0.573543
0.573476
0.573444
0.573429
0.573421
0.573418
0.633597
0.633179
0.632981
0.632887
0.632843
0.632821
0.632811
0.632806
0.653071
0.652565
0.652324
0.652208
0.652153
0.652126
0.652113
0.652107
0.662048
0.661477
0.661202
0.661069
0.661005
0.660974
0.660959
0.660952
0.665504
0.66489
0.664591
0.664446
0.664376
0.664341
0.664325
0.664316
0.666972
0.666333
0.666019
0.665865
0.66579
0.665753
0.665735
0.665727
0.667565
0.666913
0.66659
0.666431
0.666353
0.666314
0.666295
0.666286
0.667806
0.667148
0.666821
0.666659
0.666578
0.666539
0.666519
0.66651
0.66789
0.66723
0.666901
0.666738
0.666657
0.666617
0.666597
0.666587
3.3改变迭代初始值
3.3.1将x0各分量初值置为0
增加一句代码为:
x0=zeros（20,1）;
0.333333
0.416667
0.453704
0.468943
0.475823
0.478928
0.472222
0.552662
0.563786
0.568911
0.5
0.571759
0.604552
0.619567
0.626559
0.581019
0.618441
0.636156
0.644499
0.62365
0.643004
0.652308
0.624807
0.645062
0.654947
0.625
0.645689
0.655883
0.645817
0.656162
0.645833
0.656235
0.656249
0.480365
0.481035
0.48135
0.481499
0.48157
0.481604
0.481621
0.57129
0.572406
0.572933
0.573184
0.573304
0.573361
0.573389
0.629838
0.631388
0.632124
0.632476
0.632644
0.632725
0.632764
0.648466
0.650356
0.651261
0.651696
0.651905
0.652006
0.652055
0.656778
0.658931
0.65997
0.660472
0.660715
0.660833
0.660891
0.659753
0.662092
0.663229
0.663783
0.664052
0.664184
0.664248
0.660897
0.663356
0.664561
0.665152
0.665441
0.665582
0.665652
0.661286
0.663818
0.665067
0.665682
0.665985
0.666134
0.666207
0.661413
0.663984
0.665258
0.665888
0.666199
0.666352
0.666428
0.661447
0.664035
0.66532
0.665957
0.666272
0.666427
0.666504
16
0.481628
0.481632
0.481634
0.573402
0.573409
0.573412
0.632783
0.632792
0.632797
0.652079
0.65209
0.652096
0.660918
0.660932
0.660939
0.664279
0.664294
0.664302
0.665686
0.665702
0.66571
0.666242
0.66626
0.666269
0.666465
0.666483
0.666492
0.666541
0.66656
0.666569
【分析】
从数据中可以看出，当迭代的初值变化了，达到相同精度所需要的迭代次数也变化了。
3.3.2将各分量初始值置为10
直接在下面给出数据结果
2.833333
1.527778
0.91088
0.675347
0.568978
0.522036
4.5
2.138889
1.274306
0.886381
0.717544
0.640258
5.333333
2.652778
1.555556
1.054977
0.829347
0.724922
2.930556
1.703704
1.149884
0.886445
0.763505
1.792824
1.204282
0.922108
0.786414
1.827546
1.232446
0.941607
0.799154
1.833333
1.24566
0.951517
0.806292
1.249518
0.956147
0.809893
1.25
0.957891
0.811558
0.958293
0.812201
0.500453
0.490492
0.485828
0.483632
0.48259
0.482094
0.481856
0.604785
0.588229
0.580454
0.576775
0.575025
0.574189
0.573788
0.676331
0.653479
0.642672
0.637531
0.635075
0.633897
0.633331
0.705174
0.677509
0.664299
0.657976
0.654937
0.653473
0.652766
0.721378
0.690096
0.675037
0.667768
0.664254
0.662552
0.661726
0.729901
0.696211
0.679836
0.67187
0.667994
0.666105
0.665185
0.734672
0.69952
0.682274
0.673825
0.669687
0.667661
0.666669
0.737255
0.701287
0.68352
0.67476
0.670446
0.668324
0.667282
0.738557
0.702202
0.684155
0.675215
0.670796
0.668615
0.66754
0.739081
0.70259
0.684423
0.675403
0.670934
0.668725
0.667635
0.
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