Liu Dongdong

Liu Dongdong
GuangDong University of Technology · School of Mathematics and Statistics

Doctor of Philosophy

About

12
Publications
847
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236
Citations
Additional affiliations
June 2018 - present
Guangdong University of Technology, Guangzhou, China
Position
  • Guangzhou, China
August 2015 - April 2018
University of Macau
Position
  • Macau, China

Publications

Publications (12)
Article
In this paper, we define a system of cyclic stationary probability distribution equations for a second order Markov chain process in case that all states are independent each other, which improves the system of equations in [W. Li, and M.K. Ng, On the limiting probability distribution of a transition probability tensor, Linear and Multilinear Algeb...
Article
In this paper, we propose a new preconditioned SOR method for solving the multi-linear systems whose coefficient tensor is an \({\mathcal{M}}\)-tensor. The corresponding comparison for spectral radii of iterative tensors is given. Numerical examples demonstrate the efficiency of the proposed preconditioned methods.
Article
In this paper, we revisit the multilinear PageRank problem. Under the framework of tensor, we establish several new and tighter uniqueness conditions for the multilinear PageRank vector. Meanwhile, a refined error bound for the inverse iteration as well as the new perturbation bounds under different norms, which improve the existing ones in the cur...
Article
In this paper, we propose several relaxation algorithms for solving the tensor equation arising from the higher‐order Markov chain and the multilinear PageRank. The semi‐symmetrization technique on the original equation is also employed to modify the proposed algorithms. The convergence analysis is given for the proposed algorithms. It is shown tha...
Article
It is known that the spectral radius of the iterative tensor can be seen as an approximate convergence rate for solving multi-linear systems by tensor splitting iterative methods. So in this paper, first we give some spectral radius comparisons between two different iterative tensors. Then, we propose the preconditioned tensor splitting method for...
Article
We discuss the uniqueness and the perturbation analysis for sparse non-negative tensor equations arriving from data sciences. By two different techniques, we may get better ranges of parameters to guarantee the uniqueness of the solution of the tensor equation. On the other hand, we present some perturbation bounds for the tensor equation. Numerica...
Article
Full-text available
In this paper, we consider finding fixed point of nonexpansive mappings by Mann algorithms combined with inertial extrapolation and some accelerating techniques. Previous attempts for such approach require assumptions on the generated sequence to guarantee convergence. Such assumptions are not easy to check in practice. Inspired by some recent work...
Article
In this paper, we establish new weighted integral inequalities by considering polynomials which are orthogonal in a weighted sense. These inequalities generalize some results established recently. They are applied to study exponential stability of some time-delay systems under the framework of linear matrix inequalities. Numerical tests are given t...
Article
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...
Article
In this paper, firstly, we introduce the variant tensor splittings, and present some equivalent conditions for a strong M-tensor based on the tensor splitting. Secondly, the existence and uniqueness conditions of the solution for multi-linear systems are given. Thirdly, we propose some tensor splitting algorithms for solving multi-linear systems wi...
Article
The uniqueness of multilinear PageRank vectors is discussed, and the new uniqueness condition is given. The new results are better than the one given in the work of Gleich et al. published in SIAM J Matrix Anal Appl. 2015;36;1409-1465. Numerical examples are given to demonstrate the new theoretical results.
Article
In this paper, we consider the Z-eigenpair of a tensor, in particular, an irreducible nonnegative tensor. We present some bounds for the eigenvector and Z-spectral radius. The proposed bounds improve some existing ones. An example with practical applications is given to show the proposed bound.

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