Abstract: Based on the conjugate gradient (CG) algorithm, the constrained matrix equation 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.
Abstract: In this paper, according to the classical algorithm
LSQR for solving the least-squares problem, an iterative method is
proposed for least-squares solution of constrained matrix equation. By
using the Kronecker product, the matrix-form LSQR is presented to
obtain the like-minimum norm and minimum norm solutions in a
constrained matrix set for the symmetric arrowhead matrices. Finally,
numerical examples are also given to investigate the performance.
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.
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.
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.
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.
Abstract: Many exist studies always use Markov decision
processes (MDPs) in modeling optimal route choice in
stochastic, time-varying networks. However, taking many
variable traffic data and transforming them into optimal route
decision is a computational challenge by employing MDPs in
real transportation networks. In this paper we model finite
horizon MDPs using directed hypergraphs. It is shown that the
problem of route choice in stochastic, time-varying networks
can be formulated as a minimum cost hyperpath problem, and
it also can be solved in linear time. We finally demonstrate the
significant computational advantages of the introduced
methods.
Abstract: The real representation of the quaternionic matrix is
definited and studied. The relations between the positive (semi)define
quaternionic matrix and its real representation matrix are presented.
By means of the real representation, the relation between the positive
(semi)definite solutions of quaternionic matrix equations and those of
corresponding real matrix equations is established.
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.
Abstract: A novel path planning approach is presented to solve
optimal path in stochastic, time-varying networks under priori traffic
information. Most existing studies make use of dynamic programming
to find optimal path. However, those methods are proved to
be unable to obtain global optimal value, moreover, how to design
efficient algorithms is also another challenge.
This paper employs a decision theoretic framework for defining
optimal path: for a given source S and destination D in urban transit
network, we seek an S - D path of lowest expected travel time
where its link travel times are discrete random variables. To solve
deficiency caused by the methods of dynamic programming, such as
curse of dimensionality and violation of optimal principle, an integer
programming model is built to realize assignment of discrete travel
time variables to arcs. Simultaneously, pruning techniques are also
applied to reduce computation complexity in the algorithm. The final
experiments show the feasibility of the novel approach.