# Prof. Dr. Minghui Wang

**Committee:**International Scientific Committee of Electronics and Communication Engineering

**University:**Qingdao University of Science and Technology

**Department:**Mathematics

**Research Fields:**quaternionic linear equations, Real representation, iterative algorithm.,

## Publications

##### 10 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

*AXB=C*and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

**Keywords:**
Iterative Method,
Conjugate Gradient algorithm,
Symmetric arrowhead matrix

##### 9 An Iterative Method for the Symmetric Arrowhead Solution of Matrix Equation

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

**Keywords:**
Iterative Method,
like-minimum norm,
minimum norm,
Symmetric arrowhead matrix,
Algorithm LSQR

##### 8 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

**Authors:**
Minghui Wang,
Juntao Zhang

**Abstract:**

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

**Keywords:**
Convergence,
Inversion-free method,
Hermitian positive definite solution,
Maximal solution

##### 7 An Iterative Method for Quaternionic Linear Equations

**Authors:**
Bin Yu,
Minghui Wang,
Juntao Zhang

**Abstract:**

By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.

**Keywords:**
iterative algorithm,
Real representation,
Quaternionic linear equations

##### 6 Iterative Methods for An Inverse Problem

**Authors:**
Minghui Wang,
Shanrui Hu

**Abstract:**

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

**Keywords:**
Iterative methods,
doubly center matrix,
electric network theory,
least-square problem

##### 5 A Novel Approach of Route Choice in Stochastic Time-varying Networks

**Authors:**
Siliang Wang,
Minghui Wang

**Abstract:**

**Keywords:**
hypergraphs,
Markov decision processes (MDPs),
stochastictime-varying networks,
route choice

##### 4 Optimal Route Policy in Air Traffic Control with Competing Airlines

**Authors:**
Siliang Wang,
Minghui Wang

**Abstract:**

This work proposes a novel market-based air traffic flow control model considering competitive airlines in air traffic network. In the flow model, an agent based framework for resources (link/time pair) pricing is described. Resource agent and auctioneer for groups of resources are also introduced to simulate the flow management in Air Traffic Control (ATC). Secondly, the distributed group pricing algorithm is introduced, which efficiently reflect the competitive nature of the airline industry. Resources in the system are grouped according to the degree of interaction, and each auctioneer adjust s the price of one group of resources respectively until the excess demand of resources becomes zero when the demand and supply of resources of the system changes. Numerical simulation results show the feasibility of solving the air traffic flow control problem using market mechanism and pricing algorithms on the air traffic network.

**Keywords:**
Air Traffic Control,
Nonlinear Programming,
Marketmechanism,
Route policy

##### 3 Optimal Path Planning under Priori Information in Stochastic, Time-varying Networks

**Authors:**
Siliang Wang,
Minghui Wang,
Jun Hu

**Abstract:**

**Keywords:**
stochastic,
pruning method,
time-varying networks,
optimal path planning

##### 2 On Positive Definite Solutions of Quaternionic Matrix Equations

**Authors:**
Minghui Wang

**Abstract:**

**Keywords:**
Matrix Equation,
Quaternionic matrix,
Real representation,
positive (semi)definite solutions

##### 1 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application

**Authors:**
Minghui Wang

**Abstract:**

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

**Keywords:**
iterative algorithm,
Matrix Equation,
bisymmetric matrix,
least squares problem,
like-minimum norm