finish the script by insert commands to solve the linear system of equations using gauss-seidel iteration solver. in matlab

You can use the following script to solve a system of linear equations using Gauss-Seidel iteration solver in MATLAB:

main.m
% Define coefficient matrix A, right hand side vector b and initial guess x
A = [4, -1, 0; 2, 8, -1; 0, 1, 4];
b = [12; 1; 4];
x = [0; 0; 0];

% Define tolerance and maximum iterations
tol = 1e-6;
max_iterations = 1000;

% Perform Gauss-Seidel iteration
for iteration = 1:max_iterations
    x_previous = x;
    for i = 1:length(b)
        x(i) = (b(i) - A(i,1:i-1) * x(1:i-1) - A(i,i+1:end) * x_previous(i+1:end)) / A(i,i);
    end
    % Check for convergence
    if norm(x - x_previous) < tol
        fprintf('Gauss-Seidel method converged after %d iterations.\n', iteration);
        fprintf('Solution:\n');
        disp(x);
        return
    end
end

% Gauss-Seidel method failed to converge
fprintf('Gauss-Seidel method failed to converge after %d iterations.\n', max_iterations);
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In this script, you can define the coefficient matrix A, right hand side vector b and initial guess x. You can also specify the tolerance tol and maximum iterations max_iterations.

The Gauss-Seidel iteration is performed using two nested loops. The outer loop runs for a maximum of max_iterations iterations. The inner loop updates each component of x using the current values of the other components. The updated value of x at each iteration is stored in x_previous, so that the norm of their difference can be computed to test for convergence.

If the method converges within the specified tolerance, the script outputs the final solution. If the method fails to converge within the specified number of iterations, the script prints a warning message.