Algorithm 5.2.

Alternating least squares ALS

\begin{array}{l} I n p u t s : Data matrix X, initial iterates A_{0} and B_{0}, and k = 0. \\ O u t p u t s : (A^{*}, B^{*}) = \arg \min_{A, B} F (A, B) \\ R e p e a t u n t i l C o n v e r g e n c e \\ f o r i=1 to m d o \\ A_{i} \leftarrow {(\sum_{j \in Ω_{i}} B_{j} B_{j}^{T})}^{- 1} (\sum_{j \in Ω_{i}} X_{i j} B_{j}) \\ e n d f o r \\ f o r j = 1 to n d o \\ B_{j} \leftarrow {(\sum_{i \in Ω_{j}} A_{i} A_{i}^{T})}^{- 1} (\sum_{i \in Ω_{j}} X_{i j} A_{i}) \\ e n d f o r \end{array}