(untitled) (Journal of Computational Mathematics, 2021)
We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions: given matrices AR^n× n and BR^n× k, n>k, minimize the residual \|AQ-B\|_F over the Stiefel manifold of orthonormal matrices. Theoretical analysis on necessary conditions and sufficient conditions for optimal solutions of the unbalanced Procrustes problem is given.