3-Ma’ruza: Chiziqli algebraik tenglamalar sistemasini taqribiy yechish Reja

3.19-misol. Quyidagi chiziqli tenglamalar sistemasi =10^-3 aniqlikda Zeydel usuli bilan yeching.

Yechish. Bu tenglamalar sistemasi uchun (3.41) shartning bajarilishini tekshirib ko‘rish qiyin emas. Uni (3.40) ko‘rinishga keltiramiz.
x₁=(21.70-1.2x₂-2.1x₃-0.9x₄)/20.9
x₂=(27.46-1.2x₁-1.5x₃-2.5x₄)/21.2
x₃=(28.76-2.1x₁-1.5x₂-1.3x₄)/19.8
x₄=(49.72-0.9x₁-2.5x₂-1.3x₃)/32.1
boshlang‘ich vektorni

kabi tanlab, Zeydel usulini qo‘llaymiz.
K=1 deb, birinchi yaqinlashishni topamiz:
=(21.7-1.1 -2.1 -0.9 )/20.9=
=(21.7-1.56-3.045-1.395)/20.9=0.7512
=(27.46-1.2 -1.5 -2.5 )/21.2=
=(27.46-0.900-2.175-3.875)=0.9674
=(28.76-2.1 -1.5 -1.3 )/19.8=
=(28.76-1.575-1.455-2.013)=1.1977
=(49.72-0.9 -2.5 -1.3 )/32.1=
=(49.72-0.675-2.425-1.56)=1.4037

K=2 bo‘lganda: =13.76062/20.9=0,6558
=21.9902/21.2=0.9996
=23.75180/19,8=1,19959
=44.93971/32.1=1.4000

K=3 bo‘lganda: =13.7213/20.9=0.6557
=21.200528/21.2=1.00002
=23.759844/19.8=1.19999
=44.939909/32.1=1.4000

Bu qadam uchun yaqinlashish sharti bajarildi, demak, berilgan aniqlikdagi yechim:

CHiziqli tenglamalar sistemasini Zeydel usuli bilan hisoblash dasturini beramiz:
{ * --------3.12- Paskal tilida dastur --------- *}
uses crt;
label 40,90,100;
var
n,i,j:integer;
c,c1:real;
a:array[1..5,1..5] of real;