Berdaq nomidagi qoraqolpoq davlat universiteti fizika-matematika fakulteti

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)

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