Gauss Seidel Method with Relaxation

I am working on a matlab code using the Gauss Seidel method with relaxation to solve a system to a specified tolerance of es = 5%.

Something is wrong with my code, as I am not getting the correct output. Any help would be appreciated.

    % function x=GaussSeidel_Relax_Example(lambda, es)
% Gauss-Seidel for a 3-by-3 linear system of equations
%
%--Input
%  lambda: relaxation parameter
%  es: error tolerance (approximate absolute percent relative error in solution)
%
%--Output
%  x:    Gauss-Seidel  linear solution (3-by-1 vector)
% Note: 1. Use the Euclidian norm (i.e. 2-norm) to compute relative error.
%       2. You may need to rearrange the linear equations to achieve diagonal dominance.
% Write your code here.
lambda = 0.7;
es = 0.5;
Eqn1_LHS = [10 2 -1];
Eqn1_RHS = 27;
Eqn2_LHS = [-3 -6 2];
Eqn2_RHS = -61.5;
Eqn3_LHS = [1 1 5];
Eqn3_RHS = -21.5;
x = [10 10 10];  % Initial guess for the solution x
error = 1;   % Initializing error
iter = 0; % number of iterations
while error > es % Running the code until actual error is greater than tolerance
    x_old = x;
    x(1,1) = (1-lambda) * x(1,1) + lambda * ((Eqn1_RHS - Eqn1_LHS(1,2) * x(1,2) -    Eqn1_LHS(1,3) * x(1,3)) / (Eqn1_LHS(1,1)));
    x(1,2) = (1-lambda) * x(1,2) + lambda * ((Eqn2_RHS - Eqn2_LHS(1,1) * x(1,1) -    Eqn2_LHS(1,3) * x(1,3)) / (Eqn2_LHS(1,2)));
    x(1,3) = (1-lambda) * x(1,3) + lambda * ((Eqn3_RHS - Eqn3_LHS(1,1) * x(1,1) -    Eqn3_LHS(1,2) * x(1,2)) / (Eqn3_LHS(1,3)));
    error = norm(x - x_old) / norm(x);
    iter = iter + 1;
end
disp('Total number of iterations needed is:');
disp(iter)
  end

The output I am given is 0.4685, 8.2208, -5.9833.

The correct output is 0.608679, 7.964641, -5.976428

I think I am messing up and not fully understanding making an initial guess or initializing error. Could someone please help review the code. I keep trying to work at it, but am clearly missing something. Thank you.

Answer 1

[resul demir]

Do you have any solutions for Gauss Seidel method with relaxation with making matrix diagonally dominant ?