The Procrustes problem for orthogonal Kronecker products

Adam W. Bojanczyk, Adam Lutoborski

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The Procrustes problem for orthogonal Kronecker products is considered. Given matrices A ∈ ℝn2×k2, T ∈ ℝn2×n2, n ≥ k, we minimize the Frobenius norm ∥T(Q ⊗ Q) - A ∥ for all orthogonal Stiefel matrices Q ∈ ℝn×k, QT Q = Ik. We introduce and implement left and right relaxation methods for minimization. Numerical results for the data in general and Kronecker product form are given to illustrate convergence of both methods.

Original languageEnglish (US)
Pages (from-to)148-163
Number of pages16
JournalSIAM Journal on Scientific Computing
Volume25
Issue number1
DOIs
StatePublished - Sep 2003

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Keywords

  • Kronecker products
  • Procrustes problem
  • Relaxation methods
  • Stiefel matrices

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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