when I clicked the run button, the system shows
The matrix is not strictly diagonally dominant at row 1
The matrix is not strictly diagonally dominant at row 2
The matrix is not strictly diagonally dominant at row 3
The matrix is not strictly diagonally dominant at row 4
What dose this mean?? what's the matter with my input??
clear;clc
format compact
%% Read or Input any square Matrix
A = [-8.7673 9.4736 0 0 0;
4.7368 -8.4736 4.7368 0 0;
0 4.7368 -8.4736 4.7368 0;
0 0 4.7368 -8.4736 4.7368;
0 0 0 -9.4736 10.4736];% coefficients matrix
C = [20;20;20;20;20];% constants vector
n = length(C);
X = zeros(n,1);
Error_eval = ones(n,1);
%% Check if the matrix A is diagonally dominant
for i = 1:n
j = 1:n;
j(i) = [];
B = abs(A(i,j));
Check(i) = abs(A(i,i)) - sum(B); % Is the diagonal value greater than the remaining row values combined?
if Check(i) < 0
fprintf('The matrix is not strictly diagonally dominant at row %2i\n\n',i)
end
end
%% Start the Iterative method
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) = (C(i) - sum(A(i,j) * Xtemp)) / A(i,i);
end
Xsolution(:,iteration) = X;
Error_eval = sqrt((X - Z).^2);
end
%% Display Results
GaussSeidelTable = [1:iteration;Xsolution]'
MaTrIx = [A X C]
Hi Maria. As far as I got it without running the code, there is one error at
Check(i) = abs(A(i,i)) - sum(B);
which should rather read
for i=1:n
Check(i) = abs(A(i,i)) - sum(abs(A(i,:)));
if Check(i) < 0
fprintf('The matrix is not strictly diagonally dominant at row %2i\n\n',i)
end
or something like that, since diagonal dominance states that absolute values of diagonal elements are always greater or equal to the absolute values of the other remaining (absolute) row elements.
Moreover, it seems to me that the input matrix A in your example is not diagonal dominant, as e.g. |A(1,1)|
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