To solve the system of linear equations using the Gauss-Seidel iterative method in MATLAB, we can apply the iteration formula for a specified number of iterations. This is an example that applies 4 iterations:
% Define the coefficient matrix and the right-hand side vector
A = [1 5 -6; 3 1 5; 1 4 1];
b = [5; 23; 7];
% Define the initial guess for the solution
x0 = [0; 0; 0];
% Define the number of iterations to apply
n_iter = 4;
% Apply the Gauss-Seidel iteration formula for the specified number of iterations
x = x0;
for k = 1:n_iter
for i = 1:length(b)
x(i) = (b(i) - A(i,1:i-1)*x(1:i-1) - A(i,i+1:end)*x(i+1:end)) / A(i,i);
end
end
% Display the solution
disp(x);
The solution can be found by simply running the above code.
