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Volume 25, Issue 6
Conditions for Optimal Solutions of Unbalanced Procrustes Problem on Stiefel Manifold

Zhenyue Zhang, Yuyang Qiu & Keqin Du

J. Comp. Math., 25 (2007), pp. 661-671.

Published online: 2007-12

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  • Abstract

We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions: given matrices $A\in \mathcal{R}^{n\times n}$ and $B\in \mathcal{R}^{n\times k}$, $n>k$, 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.

  • Keywords

Procrustes problem, Stiefel manifold, Necessary condition, Sufficient condition.

  • AMS Subject Headings

65F05, 15A06.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-661, author = {}, title = {Conditions for Optimal Solutions of Unbalanced Procrustes Problem on Stiefel Manifold}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {6}, pages = {661--671}, abstract = {

We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions: given matrices $A\in \mathcal{R}^{n\times n}$ and $B\in \mathcal{R}^{n\times k}$, $n>k$, 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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8721.html} }
TY - JOUR T1 - Conditions for Optimal Solutions of Unbalanced Procrustes Problem on Stiefel Manifold 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 -

We consider the unbalanced Procrustes problem with an orthonormal constraint on solutions: given matrices $A\in \mathcal{R}^{n\times n}$ and $B\in \mathcal{R}^{n\times k}$, $n>k$, 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.

Zhenyue Zhang, Yuyang Qiu & Keqin Du. (1970). Conditions for Optimal Solutions of Unbalanced Procrustes Problem on Stiefel Manifold. Journal of Computational Mathematics. 25 (6). 661-671. doi:
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