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Gauss-Jacobi and Gauss-Siedel

  1. Jun 14, 2010 #1
    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 ?
     
  2. jcsd
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