The symmetric Procrustes problem

Higham, Nicholas J. (1988) The symmetric Procrustes problem. BIT Numerical Mathematics, 28. pp. 133-143. ISSN 1572-9125

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Abstract

The following "symmetric Procrustes" problem arises in the determination of the strain matrix of an elastic structure: find the symmetric matrix X which minimises the Frobenius (or Euclidean) norm of AX — B, where A and B are given rectangular matrices. We use the singular value decomposition to analyse the problem and to derive a stable method for its solution. A perturbation result is derived and used to assess the stability of methods based on solving normal equations. Some comparisons with the standard, unconstrained least squares problem are given.

Item Type: Article
Uncontrolled Keywords: Least squares - symmetric Procrustes problem - singular value decomposition - normal equations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Ms Lucy van Russelt
Date Deposited: 28 Jun 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/335

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