TY - JOUR
T1 - Conditions for Optimal Solutions of Unbalanced Procrustes Problem on Stiefel Manifold
AU - Zhenyue Zhang, Yuyang Qiu & Keqin Du
JO - Journal of Computational Mathematics
VL - 6
SP - 661
EP - 671
PY - 2007
DA - 2007/12
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8721.html
KW - Procrustes problem, Stiefel manifold, Necessary condition, Sufficient condition.
AB - <p style="text-align: justify;">We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions: given matrices $A\in \mathcal{R}^{n\times n}$ and $B\in \mathcal{R}^{n\times k}$, $n&gt;k$, 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.</p>