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Numerische Mathematik

, Volume 82, Issue 4, pp 599–619 | Cite as

A Procrustes problem on the Stiefel manifold

  • Lars Eldén
  • Haesun Park

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.

Mathematics Subject Classification (1991):65F20, 15A24 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Lars Eldén
    • 1
  • Haesun Park
    • 2
  1. 1. Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden; e-mail: elden@math.liu.se SE
  2. 2. Computer Science Department, University of Minnesota, Minneapolis, MN 55455, USA; e-mail: hpark@cs.umn.edu US

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