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Title: Pseudo-spectra theory of tensors and tensor polynomial eigenvalue problems
Authors: Che, ML
Li, GY
Qi, LQ 
Wei, YM
Keywords: Tensors
Tensor polynomial eigenvalue problems
Regular tensor polynomial
Backward error
Nonnegative weights
Issue Date: 2017
Publisher: North-Holland
Source: Linear algebra and its applications, 2017, v. 533, p. 536-572 How to cite?
Journal: Linear algebra and its applications 
Abstract: This paper is devoted to the extension of the epsilon-pseudo-spectra theory from matrices to tensors. Based on the definition of an eigenpair of real symmetric tensors and results on the epsilon-pseudo-spectrum of square matrices, we first introduce the epsilon-pseudo-spectrum of a complex tensor and investigate its fundamental properties, such as its computational interpretations and the link with the stability of its related homogeneous dynamical system. We then extend the epsilon-pseudo-spectrum to the setting of tensor polynomial eigenvalue problems. We further derive basic structure of the epsilon-pseudo-spectrum for tensor polynomial eigenvalue problems including the symmetry, boundedness and number of connected components under suitable mild assumptions. Finally, we discuss the implication of the epsilon-pseudo-spectrum for computing the backward errors and the distance from a regular tensor polynomial to the nearest irregular tensor polynomial.
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2017.07.026
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