-inclusion sets for eigenvalues of a tensor

In this paper, we mainly focus on new inclusion sets for eigenvalues of a tensor. First, we propose new inclusion sets for eigenvalues of a tensor, which are sharper than some existing inclusion sets, and obtain the law of distribution of the number of eigenvalues for a tensor. Second, two new classes of tensors are introduced. Third, some bounds on the spectral radii for nonnegative tensors are given. Fourth, some checkable sufficient conditions for the positive definiteness (positive semidefiniteness) of some classes of even-order real symmetric tensors are obtained.     

Reverse order law for generalized inverses of multiple operator product

In this paper, we consider the reverse order law for generalized inverses of operators on Hilbert spaces. We derive necessary and sufficient conditions for various inclusions concerning the reverse order law for generalized inverses of multiple operator product. We extend the finite dimensional results from (Wei M. Reverse order laws for generalized inverses of multiple matrix products. Linear Algebra Appl. 1999;293:13.) to infinite dimensional settings.     

Techniques to generate hyper-ideals of multilinear operators

The usual techniques to generate ideals of multilinear operators between Banach spaces fail in generating hyper-ideals in general. In this paper, we fill this gap by developing two techniques to generate hyper-ideals of multilinear operators. The techniques we develop generate new classes of multilinear operators and show that some important well-studied classes are Banach or p-Banach hyper-ideals.     

Tensor complementarity problems: the GUS-property and an algorithm

In this paper, we study the global uniqueness and solvability (GUS-property) of tensor complementarity problems (TCPs) for some special structured tensors. The modulus equation for TCPs is also proposed, and based on this equation, we develop the corresponding nonsmooth Newton’s method, which extends the existing method given in the work of Zheng H and Li W. The modulus-based nonsmooth Newton’s method for solving linear complementarity problems. J Comput Appl Math. 2015;288: 116-126. Numerical examples are given to demonstrate the efficiency of the proposed algorithm.