Perturbation Bounds for (Nearly) Orthogonally Decomposable Tensors. (arXiv:2007.09024v2 [math.NA] UPDATED)

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 …

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