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The symmetric procrustes problem

  • Part II Numerical Mathematics
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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 matrixX which minimises the Frobenius (or Euclidean) norm ofAX — B, whereA andB 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Manchester, M139PL, Manchester, England

    Nicholas J. Higham

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  1. Nicholas J. Higham
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Higham, N.J. The symmetric procrustes problem. BIT 28, 133–143 (1988). https://doi.org/10.1007/BF01934701

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  • DOI: https://doi.org/10.1007/BF01934701

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