Using MATLAB develop an Mfile for the GaussSeidel Method to

Using MATLAB, develop an M-file for the Gauss-Seidel Method to solve the system of equations listed below until the percent relative error falls below epsilon_s = 5%. x_1 + x_2 + 5x_3 = -21.5 -3x_1 - 6x_2 + 2x_3 = -61.5 10 x_1 + 2x_2 - x_3 = 27

Solution

Code is given below:

% solution of cause seidel method:

% x1+x2+5*x3 = (-21.5)

% -3*x1-6*x2+2*x3=(-61.5)

% 10*x1+2*x2-x3 =27

% initially x2=0 and x3 =0

% solution:

% x1= -21.5-x2-5*x3

% x2 = (1/6)*(61.5-3*x1+2*x3)

% x3 = 27- 10*x1+2*x2

clear;

clc

format(\'long\');

I=1;

x2(I)=0;

x3(I)=0;

e_s = 99999;

while e_s>0.05 % error within limit

x1(I+1)= -21.5-x2(I)-5*x3(I);

x2(I+1) = (1/6)*(61.5-3*x1(I)+2*x3(I));

x3(I+1) = 27- 10*x1(I)+2*x2(I);

e_1(I+1) = abs(((x1(I+1)-x1(I))/x1(I+1))*100);

e_2(I+1) = abs(((x2(I+1)-x2(I))/x2(I+1))*100);

e_3(I+1) = abs(((x3(I+1)-x3(I))/x3(I+1))*100);

e_s = max(e_1,e_2,e_3);

I = I +1 ;

end

p = length(x1);

fprintf(\' value of x1, x2 and x,3 are: %f, %f and %f\',x1(p),x2(p),x3(p));

% end of code.

% Have a Nice Day ...

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... Have a Nice Day ...

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