II.Amaliy qismi 1.Sonli misol. Masalaning qo’yilishi
Berilgan chiziqli algebraik tenglamalar sistemasini qo’shma gradeintlar usuli bilan yeching:
2. Qo’shma gradientlar usulining va qo’shma gradientlar usulining yangi variantining hisoblash algaritimlari.
Qo’shma gradientlar usuli: Bu tenglamalar sistemasini ham yuqoridagi algoritmlar bo’yicha hisoblaymiz.
1) deb olamiz;
2) bo’ladi;
3) ![](data:image/png;base64,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)
4)
5)
6)
7)
9) 0.032823
Shuning bilan yuqoridagi sistemasinig yechimini birinchi yaqinlashuvchisi topildi. Bundan so’ng, berilgan sistemasining yechimining keyingi yaqinlashuvchilarida ko’rsatilgan tartib bilan aniqlanadi. Olingan natijalar quyidagi jadvalga joylashtirilgan
|
6.19
|
3.21
|
4.28
|
6.25
|
4.95
|
0.105944
|
|
6.19
|
3.21
|
4.28
|
6.25
|
4.95
|
|
0.65579
|
0.34008
|
0.45344
|
0.66215
|
0.52442
|
|
52.0839
|
37.8122
|
54.7561
|
50.2717
|
48.3804
|
0.032823
|
|
-0.10589
|
0.04984
|
-0.0041
|
0.10719
|
-0.0317
|
|
0.79124355
|
4.7863006
|
1.3154220
|
-5.025409
|
2.1458315
|
0.198044
|
|
0.82912
|
0.20330
|
0.18002
|
0.88577
|
0.52182
|
|
3.92794
|
4.27091
|
-7.9568
|
4.12436
|
-0.72671
|
|
|
0.00629
|
0.02091
|
-0.0108
|
-0.00544
|
-0.00515
|
0.006119
|
|
-1.3664841
|
3.4336206
|
-3.386531
|
-2.6133828
|
1.9541290998
|
|
0.79559
|
0.21762
|
0.17608
|
0.92159
|
0.51184
|
0.313909
|
|
|
|
|
|
|
|
-0.00137
|
0.000341
|
-0.001582
|
-0.00054
|
0.00349
|
0.024850
|
|
0.0000246
|
0.00027719
|
0.000168624
|
0.00006223
|
-0.0000103
|
|
0.798707
|
0.224296
|
0.172697
|
0.920801
|
0.510045
|
0.302527
|
|
0.005344
|
0.001323
|
0.005908
|
0.002111
|
0.013557
|
|
0.000001
|
0.0000009
|
0.000001
|
0.0000009
|
0.0000009
|
0.025777
|
|
0.00000002
|
0.0000000702
|
0.0000065347
|
0.0000000022
|
0.0000000001
|
|
0.798378
|
0.224531
|
0.1722319
|
0.9206448
|
0.5109042
|
0.257364
|
|
0.000011
|
0.000010
|
0.000014
|
0.0000097
|
0.0000113
|
|
0.000000
|
0.000001
|
0.000000
|
0.000001
|
0.000001
|
0.000060
|
|
|
|
|
|
|
|
0.79837
|
0.22453
|
0.172232
|
0.9206449
|
0.510904
|
0.100873
|
|
0.000001
|
0.000007
|
0.000001
|
0.0000001
|
0.000005
|
Bu topilgan jadvaldagi natijalardan kelib chiqqan natija (2.15) sistemasining Qo’shma gradeintlar usuli bilan topilgan yechimini keltiramiz ![](data:image/png;base64,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)
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