Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29399
Title: Strictly nonnegative tensors and nonnegative tensor partition
Authors: Hu, SL
Huang, ZH
Qi, LQ 
Keywords: Nonnegative tensor
Spectral radius
Strict nonnegativity
Weak irreducibility
Issue Date: 2014
Source: Science China mathematics, 2014, v. 57, no. 1, p. 181-195 How to cite?
Journal: Science China Mathematics 
Abstract: We introduce a new class of nonnegative tensors-strictly nonnegative tensors. A weakly irreducible nonnegative tensor is a strictly nonnegative tensor but not vice versa. We show that the spectral radius of a strictly nonnegative tensor is always positive. We give some necessary and sufficient conditions for the six well-conditional classes of nonnegative tensors, introduced in the literature, and a full relationship picture about strictly nonnegative tensors with these six classes of nonnegative tensors. We then establish global R-linear convergence of a power method for finding the spectral radius of a nonnegative tensor under the condition of weak irreducibility. We show that for a nonnegative tensor T, there always exists a partition of the index set such that every tensor induced by the partition is weakly irreducible; and the spectral radius of T can be obtained from those spectral radii of the induced tensors. In this way, we develop a convergent algorithm for finding the spectral radius of a general nonnegative tensor without any additional assumption. Some preliminary numerical results show the feasibility and effectiveness of the algorithm.
URI: http://hdl.handle.net/10397/29399
ISSN: 1674-7283
DOI: 10.1007/s11425-013-4752-4
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