A Procrustes problem on the Stiefel manifold |
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| Authors: | Lars Eldén Haesun Park |
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| Institution: | Department of Mathematics, Link?ping University, S-581 83 Link?ping, Sweden; e-mail: elden@math.liu.se, SE
Computer Science Department, University of Minnesota, Minneapolis, MN 55455, USA; e-mail: hpark@cs.umn.edu, US
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| Abstract: | Summary. An orthogonal Procrustes problem on the Stiefel manifold is studied, where a matrix Q with orthonormal columns is to be found that minimizes for an matrix A and an matrix B with and . Based on the normal and secular equations and the properties of the Stiefel manifold, necessary conditions for a global
minimum, as well as necessary and sufficient conditions for a local minimum, are derived.
Received April 7, 1997 / Revised version received April 16, 1998 |
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| Keywords: | Mathematics Subject Classification (1991):65F20 15A24 |
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