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Perturbation analysis has been primarily considered to be one of the main issues in many fields and considerable progress, especially getting involved with matrices, has been made from then to now. In this paper, we pay our attention to the perturbation analysis subject on tensor eigenvalues under tensor-tensor multiplication sense; and also {epsilon}-pseudospectra theory for third-order tensors. The definition of the generalized T-eigenvalue of third-order tensors is given. Several classical results, such as the Bauer-Fike theorem and its general case, Gershgorin circle theorem and Kahan theorem, are extended from matrix to tensor case. The study on {epsilon}-pseudospectra of tensors is presented, together with various pseudospectra properties and numerical examples which show the boundaries of the {epsilon}-pseudospectra of certain tensors under different levels.
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that offer grea
This paper discusses the problem of symmetric tensor decomposition on a given variety $X$: decomposing a symmetric tensor into the sum of tensor powers of vectors contained in $X$. In this paper, we first study geometric and algebraic properties of s
Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over fitting and t
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses perturbative corre
Hermitian tensors are generalizations of Hermitian matrices, but they have very different properties. Every complex Hermitian tensor is a sum of complex Hermitian rank-1 tensors. However, this is not true for the real case. We study basic properties