I run this but its given me issues. Can someone assist

```matlab % Step 1: Define variables and parameters eta = 1; % Initial value of eta epsilon = 1e-5; % Convergence condition L = 3; % L value

% Step 2: Loop for iteration eta_diff = []; % Store absolute difference between eta_n+1 and eta_n iteration = 0; % Initialize iteration counter

while true iteration = iteration + 1;

    % Calculate values using the given equation
    omega = 1 / (iteration * (iteration + 1));
    zeta = 1 / (iteration + 1);
    vartheta = 1 / (iteration + 1);
    psi_eta = eta / 2;
    A = L * eta;
    J = eta;

    eta_next = vartheta * psi_eta + zeta * (eye(size(A)) - omega * A * J) * (eta + eta_next) / 2;

    eta_diff = [eta_diff, abs(eta_next - eta)];

    % Check for convergence
    if eta_diff(end) < epsilon
        break;
    end

    eta = eta_next;
end

% Step 3: Calculate convergence rate and plot iterations = 1:iteration; convergence_rate = eta_diff(2:end) ./ eta_diff(1:end-1);

figure; subplot(2,1,1); plot(iterations, eta_diff); xlabel('Number of Iterations'); ylabel('|\eta_{n+1} - \eta_n|'); title('Convergence Rate');

subplot(2,1,2); plot(iterations(2:end), convergence_rate); xlabel('Number of Iterations'); ylabel('Convergence Rate'); title('Convergence Rate');

% Print the number of iterations until convergence fprintf('Convergence achieved in %d iterations.\n', iteration); ```

[Adam]

It would help someone to answer if you could format your code properly and give an explanation to go with it. e.g. what are the 'issues'?

[John]

Ok Will do that soon

Answer 1

[MarKf]

I assume that the copy and paste of your code did not go well... but then you should've fixed it before posting.

Even after fixing it, the reason it does not run is on the line eta_next = vartheta * etc.That said, that issue means that the code likely still needs some work.

% Step 1: Define variables and parameters 
eta = 1; % Initial value of eta 
epsilon = 1e-5; % Convergence condition 
L = 3; % L value
% Step 2: Loop for iteration 
eta_diff = []; % Store absolute difference between eta_n+1 and eta_n 
iteration = 0; % Initialize iteration counter
while true 
    iteration = iteration + 1;
    % Calculate values using the given equation
    omega = 1 / (iteration * (iteration + 1));
    zeta = 1 / (iteration + 1);
    vartheta = 1 / (iteration + 1);
    psi_eta = eta / 2;
    A = L * eta;
    J = eta;
    eta_next = eta; %issue just below, as eta_next; was not yet defined
    eta_next = vartheta * psi_eta + zeta * (eye(size(A)) - omega * A * J) * (eta + eta_next) / 2; %issue is here, as eta_next; is not yet defined
    eta_diff = [eta_diff, abs(eta_next - eta)];
    % Check for convergence
    if eta_diff(end) < epsilon
        break;
    end    
    eta = eta_next; 
end
% Step 3: Calculate convergence rate and plot 
iterations = 1:iteration; 
convergence_rate = eta_diff(2:end) ./ eta_diff(1:end-1);
figure; subplot(2,1,1); 
plot(iterations, eta_diff); 
xlabel('Number of Iterations'); ylabel('|\eta_{n+1} - \eta_n|'); title('Convergence Rate');
subplot(2,1,2); 
plot(iterations(2:end), convergence_rate); 
xlabel('Number of Iterations'); ylabel('Convergence Rate'); title('Convergence Rate');

% Print the number of iterations until convergence 
fprintf('Convergence achieved in %d iterations.\n', iteration); 

Convergence achieved in 2 iterations.

[John]

Thanks. Is there anyway the graph starts at number and converges to zero depending the number of iteration?

[John]

This is what am trying to run

\eta_{n+1} = \vartheta_{n}\Psi\left(\frac{\eta_{n} + \eta_{n + 1}}{2}\right) + \zeta_{n}\left(I - \omega_{n}AJ\right)\left(\frac{\eta_{n} + \eta_{n + 1}}{2}\right)

[MarKf]

Sorry, "graph starts at number" is not very clear. It does converge to zero but the scropt is likely not working as inteded with 2 iterations. It seems that you're trying to translate a formula or another script, the mathematical problem however is ill-defined to say the least.

I don't understand this kind of scripting \eta_{n+1} (is it latex?) but whatever language that is it seems it's accessing n+1 before defining it and you can't do that with matlab (unless you preallocate the vector I guess, but that'd be nonsensse, in that case it'd probably be a different variable called with a different name). As the number of iterations increases it seems that the second plot would also get populated with data.

[John]

Yes it is latex. You can also check the one I just sent.