A new Z-eigenvalue localization set for tensors

Abstract

A new Z-eigenvalue localization set for tensors is given and proved to be tighter than those in the work of Wang et al. (Discrete Contin. Dyn. Syst., Ser. B 22(1):187-198, 2017). Based on this set, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

An eigenvalue localization set for tensors and its applications

“…Let A = (a i 1 ···im ) ∈ R [m,n] be a weakly symmetric nonnegative tensor. Then the upper bound in Theorem 6 is smaller than those in Theorem 5 of [5], Theorem 4.5 of [4] and Corollary 4.5 of [6], that is, Finally, we show that the upper bound in Theorem 6 is smaller than those in [4][5][6][7][8][9][10] by the following example. Example 2.…”

“…In this paper, we present a new Z-eigenvalue localization set Ω(A) and prove that this set is tighter than those in [4,5]. As an application, we obtain a new upper bound Ω max (A) for the Z-spectral radius of weakly symmetric nonnegative tensors, and show that this bound is sharper than those in [4][5][6][7][8][9][10] in some cases by a numerical example.…”

“…Very recently, Zhao [5] presented another Brauer-type Z-eigenvalue localization set for tensors and proved that this set is tighter than those in Theorem 1 and Theorem 2.…”

New Sufficient Condition for the Positive Definiteness of Fourth Order Tensors

“…In [11], the authors explain the definition of the smallest Z-eigenvalue and present a computational method for calculating it. Very recently, much literature has focused on the properties of Z-eigenvalues of tensors [15][16][17][18][19][20][21][22][23][24], but there are no Z-eigenvalues based sufficient conditions for the positive definiteness of an even-order real symmetric tensor.…”

Hydrothermal synthesis for high‐quality glutathione‐capped CdxZn1 – xSe and CdxZn1 – xSe/ZnS alloyed quantum dots and its application in Hg(II) sensing

“…[16] To date, Cd x Zn 1x Se alloyed QDs have been successfully prepared in either aqueous phase or organic phase. [17][18][19] Zhong et al…”