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In this paper an origin-shifted algorithm for matrix eigenvalues based on Frobenius-like form of matrix and the quasi-Routh array for polynomial stability is given. First, using Householder's transformations, a general matrix A is reduced to upper Hessenberg form. Secondly, with scaling strategy, the origin-shifted Hessenberg matrices are reduced to the Frobenius-like forms. Thirdly, using quasi-Routh array, the Frobenius-like matrices are determined whether they are stable. Finally, we get the approximate eigenvalues of A with the largest real-part. All the eigenvalues of A are obtained with matrix deflation. The algorithm is numerically stable. In the algorithm, we describe the errors of eigenvalues using two quantities, shifted-accuracy and satisfactory-threshold. The results of numerical tests compared with QR algorithm show that the origin-shifted algorithm is fiducial and efficient for all the eigenvalues of general matrix or for all the roots of polynomial.

In this paper, the conception of numerical stabilization, which is related to mantissa digits of computer and dimensions of system, is described; and several strategies for the numerical stabilization of polynomial and matrix are presented.

Recently, several proposals for the generalization of Young's SOR method to the saddle point problem or the augmented system has been presented. One of the most practical versions is the SOR-like method given by Golub et al., [(2001). SOR-like methods for augmented systems. BIT, 41, 71–85.], where the convergence and the determination of its optimum parameters were given. In this article, a full characterization of the spectral radius of the SOR-like iteration matrix is given, and an explicit expression for the optimum parameter is given in each case. The new results also lead to different results to that of Golub et al. Besides, it is shown that by the choices of the preconditioning matrix, the optimum SOR-like iteration matrix has no complex eigenvalues, therefore, it can be accelerated by semi-iterative methods.

In this article, the accelerated over-relaxation (AOR) method is generalized for solving the saddle point problem or the augmented system. The successive over-relaxation (SOR)-like method is the special case of the generalized AOR (GAOR) method. The connection between the parameters and the eigenvalues of the iteration matrix of the GAOR method is given. Therefore, a necessary and sufficient condition for the convergence of the GAOR method is derived. Numerical examples are also given to show that the GAOR method is better than the SOR-like method in certain cases.

Based on the isometric plane method for linear programming, an algorithm for integer linear programming is proposed in this paper. The algorithm can quickly obtain the optimal integer point simultaneously using isometric planes and cutting planes derived from polyhedral-cones, rounded-minimal-balls and second-rounded-balls at the highest vertex and its neighboring vertices.

In this paper task assignment and path planning for multi-target pursuit (MTP) problem are studied. The mixed- integer linear programming (MILP) of minimax assignment is formed, and a solution called Operations on Matrix is presented. The single linear programming obstacle-avoided and the "Expansible Target Size" target pursuit method modeled by linear programming (LP) is proposed to solve the path planning problem. Finally, simulation is given to show the efficiency of the method.

A new linear programming obstacle-avoided model is presented in target pursuit and obstacle-avoided problem. The obstacle-avoided model only has the linear program once for obstacle avoidance at one time step. The collision forecasting domain of vehicle and obstacle is obtained, which can prevent the happening of collision between vehicle and obstacle. In the target pursuit problem, the dynamic equation of mass point with linear damping is taken as the state equation of vehicle's motion. “Expansible Target Size” is proposed to describe the pursuit process for target. The Linear programming method is used to model and solve the obstacle-avoided pursuit problem. Finally, simulation is given to show the efficiency of the method.

In this paper, several strategies for feedback stabilization of matrix are presented via the numerical stabilization of polynomial and matrix.

In this paper the path planning for obstacle-avoided pursuit problem (OAP) is studied. The OAP models based on the mixed integer linear programming (MILP) is presented. In the OAP models, the dynamic equation of mass point with linear damping is taken as the state equation of vehiclepsilas motion. Integer variables are used to describe the relative position of vehicle and obstacles. ldquoExpansible Target Sizerdquo is proposed to describe the pursuit process for target step-by-step. ldquoPursuit Directionrdquo of vehicle is defined. The Isometric Plane Method selected integer variables is used to solve MILP pursuit problem. How to select the integer variables of inner point is also given. Finally, simulations are given to show the efficiency of the method.

Conventional vibration signals processing techniques are most suitable for stationary processes. However, most mechanical faults in machinery reveal themselves through transient events in vibration signals. That is, the vibration generated by industrial machines always contains nonlinear and non-stationary signals. It is expected that a desired time-frequency analysis method should have good computation efficiency, and have good resolution in both time domain and frequency domain. In this paper, the auto-regressive model based pseudo-Wigner-Ville distribution for an integrated time-frequency signature extraction of the machine vibration is designed, the method offers the advantage of good localization of the vibration signal energy in the time-frequency domain. Kernel principal component analysis (KPCA) is used for the redundancy reduction and feature extraction in the time-frequency domain, and the self-organizing map (SOM) was employed to identify the faults of the rotating machinery. Experimental results show that the proposed method is very effective.

The travelling salesman problem (TSP) is a typical NP-hard problem. In this paper, a well implied enumeration method for TSP is presented where the solution of the TSP is obtained by an iterative process. At each iteration, an integer linear programming is solved by the isometric surface method. The efficiency of the algorithm is dependent on that of the integer linear programming.