What is commonly referred to as the HOSVD or Tucker was developed by [[Vasilescu]] and [[Demetri Terzopoulos|Terzopoulos]] under
the name M-mode SVD.<ref name=":Vasilescu2002"/><ref name=Vasilescu2003/><ref name=":Vasilescu2005"/>
#* For <math>m=1,\ldots,M</math>, do the following:
**# Construct the mode-''m'' flattening <math>\mathcal{A}_{[m]}</math>;
** #Compute the (compact) [[singular value decomposition]] <br/><math>\mathcal{A}_{[m]} = {\bf U}_m {\bf \Sigma}_m {\bf V}^T_m </math>, and store the left singular vectors <math>{\bf U} \in \mathbb{C}^{I_m \times R_m}</math>;
#* Compute the core tensor <math>\mathcal{S}</math> via the [[mode-k multiplication|mode-m product]] <br/><math> \mathcal{S} = \mathcal{A} \times_1 {\bf U}_1^H \times_2 {\bf U}_2^H \ldots \times_m {\bf U}_m^H \ldots \times_M {\bf U}_M^H</math>
