I would like to know the different intuition to design the two algorithms to get 3rd-order tensor SVD:

• The first one is for [n1,n2,n3] = size(Y);, after Y = fft(Y,[],3);, apply SVD to the first half front slices as for i = 2 : round(n3/2) [U,S,V] = svd(Y(:,:,i),'econ'); then get X(:,:,i) = U(:,1:r)*diag(S)*V(:,1:r)'; and X(:,:,n3+2-i) = conj(X(:,:,i))
• The second is to loop for i = 1 : n3 then SVD each Y(:,:,i)

Since it seems that there is no need for the conjugation in the matrix case, I wonder where this idea comes from and is the first case more robust when generalizing to higher order tensors?

Thanks ahead for everyone’s answers!