Fast verified computation for positive solutions to M-tensor multi-linear systems and Perron vectors of a kind of weakly irreducible nonnegative tensors
Fast verified computation for positive solutions to M-tensor multi-linear systems and Perron vectors of a kind of weakly irreducible nonnegative tensors
Miyajima, Shinya1
扫码查看
点击上方二维码区域，可以放大扫码查看
作者信息
1. Iwate Univ
折叠
Abstract
Two fast numerical algorithms are proposed for computing interval vectors containing positive solutions to M-tensor multi-linear systems. The first algorithm involves only two tensor-vector multiplications. The second algorithm is iterative one, and generally gives interval vectors narrower than those by the first algorithm. We also develop two verification algorithms for Perron vectors of a kind of weakly irreducible nonnegative tensors, which we call slightly positive tensors. The first and second algorithms have properties similar to those of the two algorithms for the solutions to the M-tensor systems. We clarify relations between slightly positive tensors and other tensor classes. Numerical results show efficiency of the algorithms. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier