matlab: having generated a krylov space of a[v, h] = arnoldi(a, v1, m) update v and h after adding dak to the kth column of a in matlab

To update the Krylov space (v, h) after adding dak to the kth column of a, you can modify the existing Arnoldi algorithm steps. Here is the general procedure:

1. Generate the Krylov space (v,h) using the Arnoldi iteration:

main.m
[v, h] = arnoldi(a, v1, m);
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2. Add dak to the kth column of a and update v and h accordingly:

main.m
a(:, k) = a(:, k) + dak; % Update the kth column of A
[v, h] = arnoldi(a, v, m); % Update the Krylov space using the modified A
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Make sure that m represents the number of iterations in the Arnoldi method, v1 is the initial vector for the Krylov space, and dak is the vector to be added to the kth column of a.

By following these steps, you can update the Krylov space (v, h) after adding dak to the kth column of a in MATLAB.