The procrustes problem for orthogonal stiefel matrices

A. W. Bojanczyk; A. Lutoborski

doi:10.1137/S106482759630992X

The procrustes problem for orthogonal stiefel matrices

A. W. Bojanczyk, A. Lutoborski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

In this paper we consider the Procrustes problem on the manifold of orthogonal Stiefel matrices. Given matrices A ε ℝ^m×k, B ε ℝ^m×p, m ≥ p ≥ k, we seek the minimum of ∥A - BQ∥² for all matrices Q ε ℝ^p×k, Q^TQ = I_k×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 language	English (US)
Pages (from-to)	1291-1304
Number of pages	14
Journal	SIAM Journal on Scientific Computing
Volume	21
Issue number	4
DOIs	https://doi.org/10.1137/S106482759630992X
State	Published - 1999

Keywords

Procrustes problem
Projections on ellipsoids
Relaxation methods
Stiefel manifolds

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1137/S106482759630992X

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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.",

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AU - Lutoborski, A.

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AB - 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.

KW - Procrustes problem

KW - Projections on ellipsoids

KW - Relaxation methods

KW - Stiefel manifolds

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JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

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ER -

The procrustes problem for orthogonal stiefel matrices

Abstract

Keywords

ASJC Scopus subject areas

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