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In this paper we consider the Procrustes problem on the manifold of orthogonal Stiefel matrices. Given matrices A∈ Rm× k, B∈ Rm× p, m≥ p ≥ k, we seek the minimum of \| A- BQ\|² for all matrices Q∈ Rp× k, QTQ=Ik× k. We introduce a class of relaxation methods for generating sequences of approximations to a minimizer and offer a geometric interpretation of these methods. Results of numerical experiments illustrating the convergence of the methods are given.
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Bojańczyk et al. (1999) studied this question.
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