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 |
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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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