论文标题
对称$ H^+$ - 张量和$ M $ -TENSORS的新特征
A new characterization of symmetric $H^+$-tensors and $M$-tensors
论文作者
论文摘要
在这项工作中，我们提出了对称$ H^+$ - 张量的新特征。众所周知，当且仅当它是具有非负对角线元件的广义对角线张量时，对称张量是$ H^+$ - 张量。通过探索对角线优势属性，我们为对称张量提供了新的必要条件，使其成为$ H^+$ - 张量。基于这些条件，我们提出了一种新颖的方法，该方法允许检查张量是否为对称的$ H^+$ - 在多项式时间内。此外，这些结果可以应用于$ m $ tensors的密切相关和重要类别。特别是，这允许有效计算对称$ m $ $ tensors的最低$ h $ eigenValue。此外，我们展示了如何使用后一个结果来为两个对称$ m $ tensors的粉丝产品的最小$ h $ eigenvalue提供更严格的下限。
In this work, we present a new characterization of symmetric $H^+$-tensors. It is known that a symmetric tensor is an $H^+$-tensor if and only if it is a generalized diagonally dominant tensor with nonnegative diagonal elements. By exploring the diagonal dominance property, we derive new necessary and sufficient conditions for a symmetric tensor to be an $H^+$-tensor. Based on these conditions, we propose a novel method that allows to check if a tensor is a symmetric $H^+$-tensor in polynomial time. Moreover, these results can be applied to the closely related and important class of $M$-tensors. In particular, this allows to efficiently compute the minimum $H$-eigenvalue of symmetric $M$-tensors. Furthermore, we show how this latter result can be used to provide tighter lower bounds for the minimum $H$-eigenvalue of the Fan product of two symmetric $M$-tensors.
