full
search.png

Search

close.png

Cancel

arrow
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

Preview Full PDF 2677 25800

Cited by

google scholar semantic scholar
Export citation
  • 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

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-25-661, author = {Zhenyue Zhang, Yuyang Qiu and Keqin Du}, 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 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 -

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 and Keqin Du. (2007). Conditions for Optimal Solutions of Unbalanced Procrustes Problem on Stiefel Manifold. Journal of Computational Mathematics. 25 (6). 661-671. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard