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.
Original language | English |
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Pages (from-to) | 181-195 |
Number of pages | 15 |
Journal | Science China Mathematics |
Volume | 57 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- nonnegative tensor
- spectral radius
- strict nonnegativity
- weak irreducibility
ASJC Scopus subject areas
- General Mathematics