The solution of orthogonal Procrustes problems for a family of orthogonally invariant norms
type: Item
instance of: scholarly article
title: The solution of orthogonal Procrustes problems for a family of orthogonally invariant norms
zbMATH Open document ID: 0831.65048
DOI: 10.1007/BF02521606
published in: Advances in Computational Mathematics
publication date: 1996-02-22T00:00:00Z
review text: The orthogonal Procrustes problem is considered. The intention is to find an orthogonal matrix that most nearly performs a transformation in the least squares sense. The problem arises in a variety of applications, and the solution in the Frobenius norm is not true in general. The paper deals with an important class of orthogonality invariant norms that contains the Frobenius norm as a special case. A method which retains orthogonality is discussed. It is shown that depending on the accuracy sought, the method can be effective. It is also shown that Newton's method provides a good enough result. Two examples are described. A comparison with the method which retains orthogonality is given.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 784502
zbMATH Keywords: orthogonal Procrustes problem
zbMATH Keywords: orthogonal matrix
zbMATH Keywords: orthogonality invariant norms
zbMATH Keywords: Frobenius norm
zbMATH Keywords: Newton's method
author: G. A. Watson
reviewed by: Tzvetan Semerdjiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02521606
OpenAlex ID: W2081926135
description: scientific article; zbMATH DE number 784502