Gauss-Seidel for solving linear equations

Apply 4 iterations, by the Gauss-Seidel iterative method, to solve the system of linear equations,Check the solutions by matrix calculation.

Answer 1

[Kautuk Raj]

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.