Zhao Jianxing, Sang Caili
College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025 P.R. China.
J Inequal Appl. 2017;2017(1):59. doi: 10.1186/s13660-017-1331-1. Epub 2017 Mar 9.
A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li . (Linear Algebra Appl. 481:36-53, 2015) and Huang . (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of [Formula: see text]-tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang ., the advantage of our results is that, without considering the selection of nonempty proper subsets of [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.
给出了一种新的张量特征值定位集，并证明它比Li（《线性代数及其应用》，481:36 - 53，2015）和Huang（《不等式及其应用杂志》，2016:254，2016）所提出的定位集更精确。作为该定位集的一个应用，建立了关于[公式：见原文]-张量最小特征值的新界，并证明这些新界比一些已知结果更精确。与Huang所得到的结果相比，我们结果的优势在于，无需考虑[公式：见原文]的非空真子集的选取，就能够得到更精确的张量特征值定位集以及更精确的[公式：见原文]-张量最小特征值界。最后，给出了数值例子来验证理论结果。
