[图书][B] Tensor analysis: spectral theory and special tensors
L Qi, Z Luo - 2017 - SIAM
Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …
number of classical books on matrix analysis have been written to explore this theory. As a …
-Tensors and Some Applications
We introduce M-tensors. This concept extends the concept of M-matrices. We denote Z-
tensors as the tensors with nonpositive off-diagonal entries. We show that M-tensors must be …
tensors as the tensors with nonpositive off-diagonal entries. We show that M-tensors must be …
Solving Multi-linear Systems with -Tensors
This paper is concerned with solving some structured multi-linear systems, especially
focusing on the equations whose coefficient tensors are M M-tensors, or called M M …
focusing on the equations whose coefficient tensors are M M-tensors, or called M M …
The sparsest solutions to Z-tensor complementarity problems
Z Luo, L Qi, N Xiu - Optimization letters, 2017 - Springer
Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard
due to the nonconvexity and noncontinuity of the involved ℓ _0 ℓ 0 norm. In this paper, a …
due to the nonconvexity and noncontinuity of the involved ℓ _0 ℓ 0 norm. In this paper, a …
Properties of some classes of structured tensors
In this paper, we extend some classes of structured matrices to higher-order tensors. We
discuss their relationships with positive semi-definite tensors and some other structured …
discuss their relationships with positive semi-definite tensors and some other structured …
Global uniqueness and solvability for tensor complementarity problems
XL Bai, ZH Huang, Y Wang - Journal of Optimization Theory and …, 2016 - Springer
Recently, the tensor complementarity problem has been investigated in the literature. An
important question involving the property of global uniqueness and solvability for a class of …
important question involving the property of global uniqueness and solvability for a class of …
Tensor complementarity problems—part I: basic theory
Tensors (hypermatrices) are multidimensional analogs of matrices. The tensor
complementarity problem is a class of nonlinear complementarity problems with the involved …
complementarity problem is a class of nonlinear complementarity problems with the involved …
Tensor complementarity problem and semi-positive tensors
In this paper, we prove that a real tensor is strictly semi-positive if and only if the
corresponding tensor complementarity problem has a unique solution for any nonnegative …
corresponding tensor complementarity problem has a unique solution for any nonnegative …
Solving the system of nonsingular tensor equations via randomized Kaczmarz-like method
A great deal of attention has been paid to solve the system of tensor equations in recent
years for its applications in various fields. In this paper, the Kaczmarz-like method, which is …
years for its applications in various fields. In this paper, the Kaczmarz-like method, which is …