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🔗 Source: opus.bibliothek.uni-augsburg.de
📊 Size: 1.74 MB
👤 Author: Henrik Eisenmann
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Summary

The relative distance in Frobenius norm of a real symmetric order-d tensor of rank-two to its best rank-one approximation is upper bounded by √1 − (1 − 1/d)d−1. This bound is achieved by determining the minimal possible ratio between spectral and Frobenius norm for symmetric tensors of border rank two, which equals (1 − 1/d)(d−1)/2. These bounds also hold for arbitrary real rank-two tensors. The maximum relative distance of a real rank-two tensor to the set of rank-one tensors is bounded by √1 − (1 − 1/d)d−1, with equality achieved for a specific symmetric tensor. As d approaches infinity, the bounds imply that the maximum relative distance and the minimal ratio between spectral and Frobenius norm are bounded independently of d.

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The relative distance in Frobenius norm of a real symmetric order-d tensor of rank-two to its best rank-one approximation is upper bounded by √1 − (1 −...

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  • File Format: PDF
  • File Size: 1.74 MB
  • Pages: 17
  • Language: EN
  • Author: Henrik Eisenmann
  • Total Downloads: 60
  • Last Updated: 6 days ago

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