Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/11591
Title: Perturbation bounds of tensor eigenvalue and singular value problems with even order
Authors: Che, M
Qi, L 
Wei, Y
Keywords: Algebraic simple
Mode-k tensor polynomial eigenvalue
Mode-symmetric embedding
Mode-symmetry
Nonsingular tensor
Tensor generalized eigenvalue
Tensor generalized singular value
Tensor quadratic eigenvalue
Issue Date: 2015
Publisher: Taylor & Francis
Source: Linear and multilinear algebra, 2015 How to cite?
Journal: Linear and multilinear algebra 
Abstract: The main purpose of this paper is to investigate the perturbation bounds of the tensor eigenvalue and singular value problems with even order. We extend classical definitions from matrices to tensors, such as, (Formula presented.)-tensor and the tensor polynomial eigenvalue problem. We design a method for obtaining a mode-symmetric embedding from a general tensor. For a given tensor, if the tensor is mode-symmetric, then we derive perturbation bounds on an algebraic simple eigenvalue and Z-eigenvalue. Otherwise, based on symmetric or mode-symmetric embedding, perturbation bounds of an algebraic simple singular value are presented. For a given tensor tuple, if all tensors in this tuple are mode-symmetric, based on the definition of a (Formula presented.)-tensor, we estimate perturbation bounds of an algebraic simple polynomial eigenvalue. In particular, we focus on tensor generalized eigenvalue problems and tensor quadratic eigenvalue problems.
URI: http://hdl.handle.net/10397/11591
ISSN: 0308-1087
EISSN: 1563-5139
DOI: 10.1080/03081087.2015.1074153
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