Web: http://arxiv.org/abs/2007.09024

Jan. 24, 2022, 2:10 a.m. | Arnab Auddy, Ming Yuan

stat.ML updates on arXiv.org arxiv.org

We develop deterministic perturbation bounds for singular values and vectors
of orthogonally decomposable tensors, in a spirit similar to classical results
for matrices such as those due to Weyl, Davis, Kahan and Wedin. Our bounds
demonstrate intriguing differences between matrices and higher-order tensors.
Most notably, they indicate that for higher-order tensors perturbation affects
each essential singular value/vector in isolation, and its effect on an
essential singular vector does not depend on the multiplicity of its
corresponding singular value or its …

arxiv math

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