Summary.
An orthogonal Procrustes problem on the Stiefel manifold is studied, where a matrix Q with orthonormal columns is to be found that minimizes \(\| AQ-B\|_{\rm F}\) for an \(l \times m\) matrix A and an \(l \times n\) matrix B with \(l \geq m\) and \(m > n\). Based on the normal and secular equations and the properties of the Stiefel manifold, necessary conditions for a global minimum, as well as necessary and sufficient conditions for a local minimum, are derived.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received April 7, 1997 / Revised version received April 16, 1998
Rights and permissions
About this article
Cite this article
Eldén, L., Park, H. A Procrustes problem on the Stiefel manifold. Numer. Math. 82, 599–619 (1999). https://doi.org/10.1007/s002110050432
Issue Date:
DOI: https://doi.org/10.1007/s002110050432