Question

Please answer in Matlab, thank you!

Gauss-Seidel method Exercise: 1. Find the roots of following simultaneous equations using the Gauss-Seidel method. 10x+2y-2z-18 4x+2y-z--10 2x-3y+ 10z=5 2. 2x1 + 6x2 + x3 = -x2+ 7x36 3. 2x7x2 tx 19 x3x2 +12 3 31 4. 25x + 5y + z =106.8 64x +8y z 177.2 144x +12y +z 279.2

Answer 1

Ans)

%====================MATLAB CODE=============

%====question1====

A=[10 2 -2;4 2 -1;2 -3 10];

b=[18;-10;5];

sol=Gauss_seidel(A,b)

%====question2====

A=[4 -1 -1;-2 6 1;-1 1 7];

b=[3;9;-6];

sol=Gauss_seidel(A,b)

%====question3====

A=[4 1 -1;2 7 1;1 -3 12];

b=[3;19;31];

sol=Gauss_seidel(A,b)

%====question4====

A=[25 5 1;64 8 1;144 12 1];

b=[106.8;177.2;279.2];

sol=Gauss_seidel(A,b)

function X=Gauss_seidel(A,b)

n = length(b);

X = zeros(n,1);

Error_eval = ones(n,1);

%% Start the Iterations

iteration = 0;

while max(Error_eval) > 0.001

iteration = iteration + 1;

Z = X; % save current values to calculate error later

for i = 1:n

j = 1:n; % define an array of the coefficients' elements

j(i) = []; % eliminate the unknow's coefficient from the remaining coefficients

Xtemp = X; % copy the unknows to a new variable

Xtemp(i) = []; % eliminate the unknown under question from the set of values

X(i) = (b(i) - sum(A(i,j) * Xtemp)) / A(i,i);

end

Xsolution(:,iteration) = X;

Error_eval = sqrt((X - Z).^2);

end

end

%========================================

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