Jingguo Qu

Inverse Eigenvalue Problem for Real Symmetric Five-Diagonal Matrix

In this paper, a kind of inverse eigenvalue problem which is the reconstruction of real symmetric five-diagonal matrix by there different eigenpairs is proposed. Given there distinguished eigenpairs, using the special computational relationship of Jacobi matrix and symmetric five-diagonal matrix, the solvability of the problem is discussed, and the sufficient and necessary conditions for the existence of a solution of this problem, as well as the analytic formula of this solution, are derived. Furthermore, to prove the theory, an appropriate numerical experiment is given by programming.

The resources purchase quantity algorithm based on the shadow price and its application in the enterprise management

The shadow price, which is determined for certain economic development goal to realize, can reflect the resources true value compared to the market price and promote to use the economical price of the resources reasonably. In this paper we design a resources purchase quantity algorithm which is based on the shadow price theoretical, A mathematical model and computer model simulation, establish a mathematical model and use computer to simulate. Finally this paper elaborates how enterprise management is instructed using the shadow price theory by the concrete example in order to raise enterprises economic efficiency.

Wavelet Boundary Element Method for Numerical Solution of Laplace Equation

Using wavelet boundary element method to solve Laplace equation, the purpose is to solve the difficulties of singular integrals in natural boundary element method, reduce computation and improve accuracy. The basic idea is that the differential equation is matched by an equivalent variational problem after natural boundary element naturalization, then use wavelet interpolation method to discrete it, and obtain the stiffness matrix which has a unique advantage, so that we can greatly reduce the computation. In this chapter, Shannon wavelet scaling functions are used as basis functions, applied to the natural boundary element method to solve the harmonic equation boundary value problems on the half-plane.

Computer simulation of the grey system prediction method and its application in water quality prediction

The water quality prediction is an important basis to implement water pollution control programs. In this paper, the gray system method is used to build a mathematical model of water quality prediction for the Yangtze River and using computer to simulate it to complete the implementation of the method for solving the model. Finally we find the method to solve problem of predicting the water quality of Yangtze River. The key problems are focused on the following two issues. (1) If we do not take more effective control measures, we make prediction analysis of the future development trendbased on past data. (2). According to the prediction analysis, we use computer to simulate that how much sewage we need to address each year.

The Study of the Solution on Multi-objective Linear Programming Problem under Fuzzy

This paper mainly presents the general model and solution of multi-objective linear programming problem under fuzzy constraint and An illustrative example is provided to demonstrate the approach. Also multi-objective fuzzy linear programming problem which contains the solution to the objective function with fuzziness or both the objective function and the constraint condition with fuzziness in multi-objective linear programming problem is discussed.

Computer simulation of fuzzy comprehensive evaluation and its application in water quality evaluation

The water quality assessment is an important basis for implementing water pollution control planning. In this paper, we use fuzzy comprehensive evaluation method to build a mathematical model of the Yangtze River Water Quality Assessment. Finally we find the method to solve the water pollution situation of the Yangtze River by comprehensive evaluation. We seek the model solving by computer simulation.The key problems are focused on the following two issues: (1) Makeing a comprehensive quantitative evaluation of Yangtze River water quality in the past two years and analyzing the water pollution situation in various regions. (2) Researching, analysising the permanganate index of major pollutants over the Yangtze River for nearly a year and ammonia nitrogen source is mainly in what areas.

Computer simulation of QR algorithm and its application in the matrix eigenvalue problem

The algorithm is a new approach for solving eigenvalue problem which is based on the P (p, q, w) rotation transform; it is the effective way for solving all the eigenvalues and eigenvectors of the general matrix at present, and it is applicable to both cases of the symmetric matrix and non-symmetric matrix. The method uses Householder matrix, first matrix A is transformed into a symmetric tridiagonal matrix, and then use computer simulation for QR algorithm to achieve the eigenvalues of symmetric triangular matrix. QR Algorithm is one of the most effective ways for solving all the eigenvalues and eigenvectors of the small and medium sized matrix at present, and it has good stability and rapid convergence speed.

Divide and conquer algorithm for computer simulation and application in the matrix eigenvalue problem

DC is a divide and conquers method for short. Its basic idea is to divide the given real symmetric tridiagonal matrix A into two lower-order submatrix A1 , A2 first, then glue the eigenvalues of the two submatrixes together and find the eigenvalue and eigenvector of the original symmetric triangular matrix by means of some calculations. It is that we solve the submatrix eigenvalue problem, and then pose a question easy to answer than the original eigenvalue problem. Finally we uses computer to simulate, using mathematical software programming to solve the elgenvalues of each submatrix separately.

The Research of Optimization Model Based on Airplane Seating Problem

According to the problem of boarding time arranged, this paper first uses an implicit enumeration method, then checks for all possible programs to conduct a preliminary screening and gets a better boarding time arranged in steps. Secondly, we establish an analytic hierarchy model; in accordance with three typical of mill type (Small aircraft A320, medium-sized A757-300 aircraft and large aircraft A380), building mutual comparison matrix. Finally we get the optimal results.

Research on Elasto-plastic Contact with Friction Multipole BEM and Rolling Process

It is a highly nonlinear problem of 3-D elasto-plastic contact with friction. To obtain the key information about the real size, displacement and traction in contact zone, the elements in contact and plastic zone should be subdivided. However, the increase of degrees of freedom is limited by the problem-solving scale when traditional BEM is used, for a larger memory size is required and the solution procedure costs too long CPU time. In this paper, based on 3-D elasto-plastic contact with friction Multipole BEM adopting Mathematical Programming, we developed the latest 3-D elasto-plastic contact with friction Multipole BEM and source Programs, and numerical experiment is carried out. Numerical experiment shows that with this new method, the need of computer memory size is only one hundredth of the traditional one, which makes the large-scale computing of subdivided elements possible and improves the computational precision