Question

Following systems of equations are given 18$x_1$ - 2$x_2$ - 3$x_3$ = 3800 7$x_3$ - 4$x_1$ - $x_2$ = 2350 15$x_2$ - 3$x_1$ - 6$x_3$ = 1200 a) Rearrange the equations to guarantee the convergence to be able to use Gauss-Siedel Method b) Starting from the initial values of $x_1^0$, $x_2^0$, $x_3^0$=0, find $x_1$, $x_2$ and $x_3$ using Gauss-Siedel Method until the approximation error for $x_3$ falls below 16% (or for 3 iterations if you cannot fall below 16%) c) Use Jacobi iteration to find $x_1$, $x_2$ and $x_3$ for the same number of iterations d) Show with which method, convergence seems to be faster and why (consider only $x_3$) Keep your calculations within maximum of 3 digits after decimal point

          Following systems of equations are given

18$x_1$ - 2$x_2$ - 3$x_3$ = 3800
7$x_3$ - 4$x_1$ - $x_2$ = 2350
15$x_2$ - 3$x_1$ - 6$x_3$ = 1200
a) Rearrange the equations to guarantee the convergence to be able to use Gauss-Siedel Method
b) Starting from the initial values of $x_1^0$, $x_2^0$, $x_3^0$=0, find $x_1$, $x_2$ and $x_3$ using Gauss-Siedel Method
until the approximation error for $x_3$ falls below 16% (or for 3 iterations if you cannot fall below
16%)
c) Use Jacobi iteration to find $x_1$, $x_2$ and $x_3$ for the same number of iterations
d) Show with which method, convergence seems to be faster and why (consider only $x_3$)
Keep your calculations within maximum of 3 digits after decimal point

Following systems of equations are given

18x1 - 2x2 - 3x3 = 3800
7x3 - 4x1 - x2 = 2350
15x2 - 3x1 - 6x3 = 1200
a) Rearrange the equations to guarantee the convergence to be able to use Gauss-Siedel Method
b) Starting from the initial values of x1^0, x2^0, x3^0=0, find x1, x2 and x3 using Gauss-Siedel Method
until the approximation error for x3 falls below 16% (or for 3 iterations if you cannot fall below
16%)
c) Use Jacobi iteration to find x1, x2 and x3 for the same number of iterations
d) Show with which method, convergence seems to be faster and why (consider only x3)
Keep your calculations within maximum of 3 digits after decimal point

Added by Shawn P.

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