
An Orthogonal Equivalence Theorem for Third Order Tensors
In 2011, Kilmer and Martin proposed tensor singular value decomposition ...
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Nondegeneracy of eigenvectors and singular vector tuples of tensors
In this article, nondegeneracy of singular vector tuples, Zeigenvectors...
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Tubal Matrix Analysis
One of the early ideas started from the 2004 workshop is to regard third...
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CPTT: using TTSVD to greedily construct a Canonical Polyadic tensor approximation
In the present work, a method is proposed in order to compute a Canonica...
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Semiparametric Tensor Factor Analysis by Iteratively Projected SVD
This paper introduces a general framework of Semiparametric TEnsor FActo...
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Inversion symmetry of singular values and a new orbital ordering method in tensor train approximations for quantum chemistry
The tensor train approximation of electronic wave functions lies at the ...
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Shifted and extrapolated power methods for tensor ℓ^peigenpairs
This work is concerned with the computation of ℓ^peigenvalues and eigen...
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TSingular Values and TSketching for Third Order Tensors
Based upon the TSVD (tensor SVD) of third order tensors, introduced by Kilmer and her collaborators, we define Tsingular values of third order tensors. Tsingular values of third order tensors are nonnegative scalars. The number of nonzero Tsingular values is the tensor tubal rank of the tensor. We then use Tsingular values to define the tail energy of a third order tensor, and apply it to the error estimation of a tensor sketching algorithm for low rank tensor approximation. Numerical experiments on real world data show that our algorithm is efficient.
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