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2006.157: The symmetric Procrustes problem

2006.157: Nicholas J. Higham (1988) The symmetric Procrustes problem. BIT Numerical Mathematics, 28. pp. 133-143. ISSN 1572-9125

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DOI: 10.1007/BF01934701


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 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.157
Deposited By:Miss Louise Stait
Deposited On:28 June 2006

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