. Author manuscript; available in PMC: 2017 Aug 18.

Published in final edited form as: J Am Stat Assoc. 2016 Aug 18;111(514):621–633. doi: 10.1080/01621459.2015.1021005

Algorithm 1.

Algorithm for Structured Matrix Completion with a given r

Input A₁₁ ∈ ℝ^m^₁×^m^₂, A₁₂ ∈ ℝ ⁽^p^₁−^m^₁×^m^₂, A₂₁ ∈ ℝ^m^₁×(^p^₂−^m^₂).
Calculate the SVD of A_•1 and A_1• to obtain A_•1 = U⁽¹⁾Σ⁽¹⁾V^(1)⊤, A_1• = U⁽²⁾Σ⁽²⁾V^(2)⊤.
Suppose M, N are orthonormal basis of U₁₁, V₁₁. We estimate the column space of U₁₁ and V₁₁ by $\hat{M} = U_{[:, 1 : r]}^{(2)}, \hat{N} = V_{[:, 1 : r]}^{(1)}$ .
Finally we estimate A₂₂ as
${\hat{A}}_{22} = A_{21} \hat{N} {({\hat{M}}^{⊤} A_{11} \hat{N})}^{- 1} {\hat{M}}^{⊤} A_{12} .$ (8)