- #1
viciado123
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Solving the system of linear equations using the methods of Gauss-Jacobi and Gauss-Siedel. Using precision of [tex]1x10^{-3}[/tex].
A=[-4 -1 2; 1 -10 6; 1 -3 -6]
B=[x1; x2; x3]
C=[1 -5 7]
A.B = C
Using Gauss-Jacobi I find:
I used x^0 = [0;0;0]. I can ?
With 11 iterations I find
[tex]X_1 = -0,762[/tex]
[tex]X_2 = -0,271[/tex]
[tex]X_3 = -1,159[/tex]
Test Stop
[tex]M_r = \frac{|-1,159 - (-1,158)|}{|-1,159|} = 8,63x10^{-4} < 1x10^{-3}[/tex]
The test is stopped for any X (x1, x2, x3) or for all ?
Using Gauss-Siedel
With 9 iterations I find
Used x^0 = [0;0;0]
[tex]X_1 = -0,758[/tex]
[tex]X_2 = -0,269[/tex]
[tex]X_3 = -1,155[/tex]
Test Stop
[tex]M_r = \frac{|-1,155 - (-1,154)|}{|-1,155|} = 8,65x10^{-4} < 1x10^{-3}[/tex]
Are correct ?
A=[-4 -1 2; 1 -10 6; 1 -3 -6]
B=[x1; x2; x3]
C=[1 -5 7]
A.B = C
Using Gauss-Jacobi I find:
I used x^0 = [0;0;0]. I can ?
With 11 iterations I find
[tex]X_1 = -0,762[/tex]
[tex]X_2 = -0,271[/tex]
[tex]X_3 = -1,159[/tex]
Test Stop
[tex]M_r = \frac{|-1,159 - (-1,158)|}{|-1,159|} = 8,63x10^{-4} < 1x10^{-3}[/tex]
The test is stopped for any X (x1, x2, x3) or for all ?
Using Gauss-Siedel
With 9 iterations I find
Used x^0 = [0;0;0]
[tex]X_1 = -0,758[/tex]
[tex]X_2 = -0,269[/tex]
[tex]X_3 = -1,155[/tex]
Test Stop
[tex]M_r = \frac{|-1,155 - (-1,154)|}{|-1,155|} = 8,65x10^{-4} < 1x10^{-3}[/tex]
Are correct ?