Liu Dongdong

• Doctor of Philosophy
• Guangdong University of Technology

In this paper, combining with the relaxation technique, we propose new preconditioned splitting methods for solving the multilinear PageRank problem. Besides, the preconditioned splitting iterative methods with Anderson acceleration are also given. Furthermore, we provide the convergence analysis of the proposed methods. Numerical experiments inclu...

In this paper, we investigate the global uniqueness and solvability for the third-order tensor linear complementarity problems. Furthermore, we transform equivalently this type of complementarity problems into the modulus equations and then we establish the modulus-based nonsmooth Newton’s method and the modulus-based tensor splitting method. Besid...

In this paper, we focus on the perturbation analysis of the largest C-eigenvalue of the piezoelectric-type tensor which could determine the highest piezoelectric coupling constant. Three perturbation bounds are presented, theoretical analysis and numerical examples show that the third perturbation bound has high accuracy when the norm of the pertur...

In this paper, we propose several improved uniqueness conditions of solution for multilinear PageRank with order-3 irreducible stochastic tensors. By considering upper and lower bounds of solutions, the refined uniqueness conditions are more effective than the existing ones. Furthermore, as an application, sharp perturbation bounds for multilinear...

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves nonnegativity for every iterative step and improves the existing ones. Furthermore, the convergence analysis...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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.

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.