The Procrustes problem for orthogonal Kronecker products

Adam W. Bojanczyk; Adam Lutoborski

doi:10.1137/S1064827501396464

The Procrustes problem for orthogonal Kronecker products

Adam W. Bojanczyk, Adam Lutoborski

Department of Mathematics

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

4 Scopus citations

Abstract

The Procrustes problem for orthogonal Kronecker products is considered. Given matrices A ∈ ℝ^n2×k2, T ∈ ℝ^n2×n2, n ≥ k, we minimize the Frobenius norm ∥T(Q ⊗ Q) - A ∥ for all orthogonal Stiefel matrices Q ∈ ℝ^n×k, Q^T Q = I_k. 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 language	English (US)
Pages (from-to)	148-163
Number of pages	16
Journal	SIAM Journal on Scientific Computing
Volume	25
Issue number	1
DOIs	https://doi.org/10.1137/S1064827501396464
State	Published - 2003

Keywords

Kronecker products
Procrustes problem
Relaxation methods
Stiefel matrices

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1137/S1064827501396464

Cite this

@article{9c1d1e43c1d043fc89f6efb46c8ce185,

title = "The Procrustes problem for orthogonal Kronecker products",

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.",

keywords = "Kronecker products, Procrustes problem, Relaxation methods, Stiefel matrices",

author = "Bojanczyk, {Adam W.} and Adam Lutoborski",

year = "2003",

doi = "10.1137/S1064827501396464",

language = "English (US)",

volume = "25",

pages = "148--163",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - The Procrustes problem for orthogonal Kronecker products

AU - Bojanczyk, Adam W.

AU - Lutoborski, Adam

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - Kronecker products

KW - Procrustes problem

KW - Relaxation methods

KW - Stiefel matrices

UR - http://www.scopus.com/inward/record.url?scp=1842459613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842459613&partnerID=8YFLogxK

U2 - 10.1137/S1064827501396464

DO - 10.1137/S1064827501396464

M3 - Article

AN - SCOPUS:1842459613

SN - 1064-8275

VL - 25

SP - 148

EP - 163

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 1

ER -

The Procrustes problem for orthogonal Kronecker products

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this