Singular value inclusion sets for rectangular tensors

New S-Type Bounds of M-Eigenvalues for Elasticity Tensors with Applications

“…Qi in [3,5,6] presented some basic studies for tensor computations and approximations. Li et al [7][8][9][10], Bu et al [11], Che et al [12], and Zhao et al [13,14] worked on analyzing the M-eigenvalues for various elasticity tensors. e authors in [15] proposed a tensor-based FTV model for the three-dimensional image deblurring problem, and some properties for Z-eigenvalues of tensor are given in [16][17][18].…”

Structured Rectangular Tensors and Rectangular Tensor Complementarity Problems

“…Let A ∈ R [p;q;m;n] be a partially symmetric rectangular tensor, and p and q are even. en, A is positive definite if and only if all of its H-singular values (or V-singular values) are positive [13][14][15][16][17][18][19]. e definition of copositive rectangular tensors is introduced in [20], which can be viewed as a generalization of copositive square tensors, and some necessary and sufficient conditions for a real partially symmetric rectangular tensor to be a copositive rectangular tensor are also given in [20].…”

Properties and calculation for <i>C</i>-eigenvalues of a piezoelectric-type tensor

“…For the case that k = s = p + q, the l k,s -singular values of a rectangular tensor reduces to the singular values of a rectangular tensor introduced in [2], which are deeply discussed in [26,31,33,34]. For the case that k = p and s = q, it was discussed in [13].…”