TY - JOUR
T1 - On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors
AU - Mo , Changxin
AU - Wei , Yimin
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 176
EP - 193
PY - 2020
DA - 2020/10
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0080
UR - https://global-sci.org/intro/article_detail/nmtma/18331.html
KW - $\mathcal{M}_z$-tensor, multi-linear system, nonnegative solution, $\mathcal{M}$-tensor, tensor equation, fixed point theory.
AB - <p style="text-align: justify;">A class of structured multi-linear system defined by strong $\mathcal{M}_z$-tensors is
considered. We prove that the multi-linear system with strong $\mathcal{M}_z$-tensors always
has a nonnegative solution under certain condition by the fixed point theory. We also
prove that the zero solution is the only solution of the homogeneous multi-linear
system for some structured tensors, such as strong $\mathcal{M}$-tensors, $\mathcal{H}^+$-tensors, strictly
diagonally dominant tensors with positive diagonal elements. Numerical examples
are presented to illustrate our theoretical results.</p>