The procrustes problem for orthogonal stiefel matrices

A. W. Bojanczyk, A. Lutoborski

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

In this paper we consider the Procrustes problem on the manifold of orthogonal Stiefel matrices. Given matrices A ε ℝm×k, B ε ℝm×p, m ≥ p ≥ k, we seek the minimum of ∥A - BQ∥2 for all matrices Q ε ℝp×k, QTQ = Ik×k. We introduce a class of relaxation methods for generating sequences of approximations to a minimizer and offer a geometric interpretation of these methods. Results of numerical experiments illustrating the convergence of the methods are given.

Original languageEnglish (US)
Pages (from-to)1291-1304
Number of pages14
JournalSIAM Journal of Scientific Computing
Volume21
Issue number4
DOIs
StatePublished - 1999

Keywords

  • Procrustes problem
  • Projections on ellipsoids
  • Relaxation methods
  • Stiefel manifolds

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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