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Perturbation bounds on the polar decomposition

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Abstract

The polar decomposition of ann ×n-matrixA takes the formA=MH whereM is orthogonal andH is symmetric and positive semidefinite. This paper presents strict bounds, (with no order terms), on the perturbationsΔM,ΔH ofM andH respectively, whenA is perturbed byΔA. The bounds onΔM can also be applied to the orthogonal Procrustes problem.

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  1. Institute of Information Processing, University of Umeå, S-90187, Umeå, Sweden

    Anders Barrlund

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  1. Anders Barrlund
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Barrlund, A. Perturbation bounds on the polar decomposition. BIT 30, 101–113 (1990). https://doi.org/10.1007/BF01932136

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  • DOI: https://doi.org/10.1007/BF01932136

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