Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2022-06-18 , DOI: 10.1016/j.aml.2022.108262 Lu-Bin Cui , Ge-Ge Lian , Jin-Yun Yuan
Recently, the existence and uniqueness of positive solution for multilinear systems with -tensor were proved by Wang et al. (2019). To expand the range of multilinear systems with positive solutions, a new class of tensors, called generalized strong -tensor, is proposed while the -tensor is a special case of the generalized strong -tensor. Under certain conditions, the existence and the uniqueness of positive (nonnegative) solutions are proved for multilinear systems with generalized strong -tensor. Finally, numerical examples are given to illustrate the theoretical results with Venn diagram for the relationship among generalized strong -tensor with certain conditions, -tensor, and strong -tensor.
中文翻译:
广义强M张量多线性系统正解的存在唯一性
最近,多线性系统正解的存在性和唯一性-张量由Wang等人证明。(2019)。为了扩大具有正解的多线性系统的范围,一种新的张量类,称为广义强-张量,建议同时-张量是广义强的一个特例-张量。在一定条件下,证明了具有广义强的多线性系统正(非负)解的存在性和唯一性-张量。最后通过数值例子说明了广义强之间关系的维恩图的理论结果。-具有特定条件的张量,-张量,强-张量。