The Procrustes Problem for Orthogonal Stiefel Matrices

@article{Bojanczyk1999ThePP,
  title={The Procrustes Problem for Orthogonal Stiefel Matrices},
  author={Adam W. Bojanczyk and Adam Lutoborski},
  journal={SIAM J. Scientific Computing},
  year={1999},
  volume={21},
  pages={1291-1304}
}
In this paper we consider the Procrustes problem on the manifold of orthogonal Stiefel matrices. Given matrices A 2 R mk , B 2 R mp , m p k, we seek the minimum of kA?BQk 2 for all matrices Q 2 R pk , Q T Q = I kk. We introduce a class of relaxation methods for generating minimizing sequences and ooer a geometric interpretation of these methods. Results of numerical experiments illustrating the convergence of the methods are given. 

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