Hi,
After going through the code given, I understand that the error you are encountering is due to the following reasons:
- In MATLAB indexing starts from 1, therefore "V(:,0)" or "beta(0)" throws error. You can use "V(:,1)" and "beta(1)". Also, "j" should start from 2 (since your V(:,1) is the initial normalized vector).
[n, k] = size(A); % n = number of rows, k = number of columns (adjust if A is square)
V = zeros(k, m+1); % Allocate space for V vectors
V(:, 1) = ones(k, 1); % Initialize V1 as ones
V(:, 1) = V(:, 1) / norm(V(:, 1), 2); % Normalize V1
beta(1) = 0; % Initialize beta_0 = 0
- The expression "alpha(j-1) = V(:,j)' .* w" performs the element wise multiplication where as for the Lancoz process you need to perform scalar multiplication of the two vectors to get the projection of "w" onto "v(:,j)".
alpha(j) = V(:, j)' * w; % scalar product for the two
- To orthogonalize the vector "w" subtract the projection of "w" onto "V(:,j)" to remove the component of "w" that lies along "V". Therefore when you are updating "w" subtract the projection of "w" onto "V(:,j)" which is "w = w - V(:,j) * alpha(j)".
w = w - V(:, j-1) * beta(j); % Subtract previous beta term
Hope this resolves your query!
