A clustering dynamic state method of maximal tree of fuzzy graph theory has been develo-ped to improve the application of a method of maximal tree of fuzzy graph theory to the clu-stering method. An application to the environmental quality assessment is giwen.

In the present paper, we give a review of pseudo-random number generators. The new methods and theory appearing in 1990's will be focused. This paper concerns with almost all kinds of generators such as the linear, nonlinear and in- versive congruential methods, Fibonacci and Tausworthe (or feedback shift regis- ter) sequences, add-with-carry and subtract-with-borrow methods, multiple prime generator and chaotic mapping, as well as the theory of combination of generators.

In this paper, the author presents a method of spline finite-points and derives acomputational scheme well suited for various types of boundary conditions. the method iseasily carried out with a computer. It bases itself on cubic B-spline, function of beamvibrations (or trigonometric funtions) and potential energy method. It is well suited forthe analysis of structure on regular regions. The method presented has great advantageover the conventional finite element method for the structrues on regular regions. Themain features of this method are matrix with narrow bandwidth and higher accuracy andmore economy in computing storage and time requirements. Moreover, a calculated ex-pample for the bending problem of plate is given, which may show the use of splinefinite-points method. This paper further introduces a simple method for the integrationof spline functions.

This paper presents the Alternating Segment Explicit-Implicit (ASE-I) method forsolving the convection-diffusion equation. The method has the obvious property ofparallelism, and is unconditionally stable. Numerical example is presented.

Computing the bounds for the greatest characteristic root of a nonnegative matrix, is important part in the theory of nonnegative matrices. It is more practical value when their bounds are expressed easily calculated function in element of matrix. In this paper, we obtain new bounds for the greatest eigenvalue of a nonnegative matrix. Compared with the results of Frobenius, the new bounds are sharper.

In this study, a mean generating function in period extrapolation is generalized. A new procedure to build a model based on the mean generating function is suggested. This model can be used to detect periods existing in time series and is suitable for long-range forecasting. The result of forecast experiments on equatorial sea surface temperature in the eastern Pacific is satistactory.

This note provides a practical modification of the Schur-Cohn-Miller theorem aboutthe location of the roots of polynomials of second order with complex coefficients. Anelementary proof of this theorem is given.

Taking the 2D Poisson equation as a working example, this paper gives a description ofthe basic idea of a new type of semidiscrete method, the Finite Element Method of Lines(FEMOL). A class of parametric FEMOL elements are derived and numerical examples aregiven.

Delaunay triangulation has been widely used in many fields such as compu- tational fluid dynamics, statistics, meteorology solid state physics, computational geometry and so on. Bowyer-Watson algorithm is a very popular one for generating Delaunay triangulation. In generating the Delaunay triangulation of a preassigned set of n points, the complexity of Bowyer-Watson algorithm can at most be reduced to O(n log n) for the simple reason that the complexity of its tree search process is O(nlog n). In this paper we suggest a tree search technique whose complexity is O(n). Noting that the order of point insertion can affect the efficiency of Bowyer- Watson algorithm, we propose a technique to optimize the point insertion process. Based on these two techniques, we obtain a fast algorithm for generating Delaunay triangulation.

The segment implicit scheme of finite difference approximation is constructed with the aid of Saulyev asymmetric schemes. Then a new alternating segment explicit-implicit method for the diffusion equation is developed, which is suitable for the computation on parallel and vector computers. The method is unconditionally stable and also gives more accurate solutions because of its better truncation error. In the numerical experiments for an example the accuracy of the method is compared with that of the AGE method (Evans and Abdullah).

In this paper, a parallel finite difference scheme for numerically solving the two-dimensional heat equation is studied. In this procedure, the domain over which the problem is defined is divided into subdomains by introducing interface points. Interface values between subdomains are found by asymmetric schemes, once these values are calculated, subdomain problems can be solved in parallel. Stability conditions and maximum norm error estimates for these procedures are derived, which demonstrate that our schemes have satisfactory stability and higher convergence order.

Deeply analyzed the conventional genetic algorithm and for its shortcomings on nonlinear optimization, heuristic genetic algorithm (HGA) is proposed. The simulated results show that the problem can be solved effectively using HGA.HGA makes some improvements on ability of global searching and locally searching. A novel way of solving nonlinear optimization that can not be realized using the general method is proposed.

In this paper, we analyze bits coding of genetic arithmetic and make use of its better local optimum operation. Also we table a proposal that we use the scheme of optimum combination of arithmetic operation of global searching and local searching based on Gray Coding and tournament selection to solve the problem of the nonlinear optimization.Using C++ program, we have tested two classical functions-Shubert and Banana. The results show that the optimized combination of genetic arithmetic operators is good for question on nonlinear optimization.

When the interface points decompose (0,1) with equal distance into multi-subdomains, there is given that a new error estimate result on the difference solu-tion of the domain decomposition algorithm developed by C.N.Dawson and others [3] for solving the heat equation. A new decomposition algorithm for the equation is also developed by using Saul'yev's asymmetric schemes at the interface points, and the error bound of the approximate solution is obtained. The results of the new algorithm is compared with that of the algorithm in [3]. Numerical experiments on the accuracy of the algorithms are also presented.

In this paper, a finite difference scheme of two-dimensional parabolic equation is constru-cted in a non-rectangular mesh by the integral method. For an arbitrary quadralateral mesh, anine--point scheme is obtained by using certain interpolation formulae. Meanwhile, an economicalscheme is established and some numerical results are given.

This article introduces several important methods of creating stochastic numbers. We apply the mixed congruential method to a two-dimension confined stable groundwater flow mathematical model with the analytical solution, the computing results are close to the analytical solution, they concide very well.

In this paper, there have analyzed three problems occurred in the incomplete Cholesky factorization with thresholds for the matrices of symmetric positive definite. First, the drop strategy is used to only a row of the matrix at a time. Based on the idea of dropping the small elements in magnitude, this strategy is extended, that is, several rows of the factor are computed and the drop strategy is exploited for these rows at a time. Second, there may occur pivots of small magnitude or even negative ones. A solution is proposed in this paper. Finally, the incomplete factorization is often difficult to implement efficiently. Several integer vectors are exploited in this paper to solve this problem. Then the efficient implementation of the modified incomplete Cholesky decomposition is in consideration. Analyses and computation experiments show that these techniques are effective.

Using Bezier curves of degree n + 1 as design curves XA(t) on one plane and Bezier curves of degree n + m + 1 as adjoint curves XB(t) on another parallel plane, the conditions of constructing developable surfaces of degree (n+ 1, n + m+ 1) are discussed.These conditions are determined by the control vextexes of the two Bezier curves and the matching functions. Furthermore, the methods for constructing developable surface of degree (n + 1, n + 2) and compositive surfaces are derived.

In this paper, an Eulerian numerical method which bases on FLIC method [1] to solvethe time--dependent equation of motion for the multi-material compressible flow of fluid is pre-sented. It is called a method of Multi-Fluid in Cell. The difference equations and computationalprocedures are very similar to those used in the PIC method [2]. However, there is a differenttransport calculation which is not required in PIC method. For a given problem in comparisonwith PIC,method our new method reduces the memory storage requirments, the calculating timeand numrical fluetuations.

The symmetric successive over relaxation- preconditioned conjugated gradient method (SSOR-PCG) is a very efficient iterative method for solving large sparse linear equations.In this paper an improved iterative format 0f the SSORPCG method is pressented,which avoids the product operation of coefficient matrix and direction vector and thus saves computation work about 8%-50%.

The particle transport Monte Carlo code MCNP had been realized the paral-lelization in MPI (Message Passing Interface) in 1999. But due to adopting the leap random number producer, some differences were existed between the parallel result and the serial result. Now the same results have been achieved by using the segment random number. The speedup of the applied problem is the liner ups to 53 in 64-processors and the parallel efficiency is up to 83% in 64-processors.

In this paper, a non-overlapping domain decomposition method is discussed for solving the exterior boundary value problem of plane elasticity equation. The exterior domain is naturally decomposed by a circle into a bounded domain and an unbounded domain. With the advantage of the natural boundary reduction, a D-N method is presented. This method is effective and geometric convergent. The convergence rate of this iteration is independent of the finite element mesh size, but dependent on the relaxation factor.

A new sorting method, the method of code-transformation, graded computing and insertional relocations is presented. Its algorithm description, time complexity and experimental results in C are given. It's proved by algorithm analysis and ex- perimental results that its time complexity is O(N) and the new sorting algorithm is better than the quick sort etc. when data are in equidistribution.

In this paper, we are concerned with the following two problems: Problem 1 we describe the set ASnE of real n -by-n anti-symmetric and persymmetric matrices such that minimize the Frobenius norm of AX - B for X, B in Rnxn; Problem 2 find the unique A in the set ASnE, satisfying ||A*- A|| - min ||A* - A||, where A* ∈ Rnxn is a given matrix, || ·|| is the Frobenius norm. We derive a general expression of the set ASnE. For Problem 2, we prove the existence and the uniqueness of the solution and provide the expression of this unique solution. We also report some numerical results to support the theory established in the paper.

This paper considers the following two problems: Problem A Given X, B e Rnxm, find A ∈ ABSn such thatAX = Bwhere ABSn is the set of all n x n anti-bisymmetric matrices. Problem B Given A ∈ Rnxn, find A e SE such thatwhere SE is the solution set of Problem A, || ?||F is the Frobenius norm.The necessary and sufficient conditions are studied for the set SE to be nonempty set. The general form of SE is given. For Problem B, the expression of the solution is provided.

A stochastic discrete model is proposed for simulating the dynamic behaviors of gas-solid systems. In the model, the motions of solid phase are obtained by calculating individual particle motions while gas flow is obtained by solving the Navier-Stokes equation including two-phase interaction. For the calculation of solid phase, the motion process of each particle is decomposed into the collision process and suspension process. Momentum conservation of collision mechanics controls the interaction between colliding particles, while the state of each suspended particle is fully dominated by the equation of force balance over that particle. Inaddition to gravity, drag force and pressure, other unclear factors are described as random force in the suspension process. As a result, the proposed model has given some numerical simulations of gas-solid systems, in which different random forces are used. It indicates that the stochastic discrete model can be used to simulate qualitatively the dynamic behaviors of gas-solid two-phase flow.

In this article,the new method with the uncertain parameter is considered for solving the augmented system.The new method is called the Generalized AOR method(GAOR).The Generalized AOR method becomes SOR-like method given by Golub et al.whenα=0.The new method is based on the splitting form of the coefficient matrix.The iterative method need choose a precondition matrix and the uncertain parameter.The functional equation between the parameters and the eigenvalues of the iteration matrix of the Generalized AOR method is given.Therefore,the necessary and sufficient condition for the convergence of the Generalized AOR method is derived by giving the restrictions imposed on the parameters.Finally,numerical computation based on a particular linear system is given,which clearly show the Generalized AOR method outperforms the SOR-like method.

This paper, with the use of Fourier transform and the filtering theory of linear timeinvariant system, reaches a conclusion that there are high-pass filter characteristicsin derivative and low-pass filter characteristics in integration after analysising fromthe view point of filtering. On the basis above, the author explores the numericalalgorithm of calculus-FFT algorithms and its adaptable condition by combining thesampling theorem of time with frequency domain, which is popularized to the numericalcomputation (NC) of non-integral-order calculus. The analysis and results of NC showthat the algorithm is convenient, fast, and applicable for the NC of low-order calculus,and specially suited to the engineering computation. It will aid in the NC, practicalutilization and error analysis of non-integer-order calculus.

This paper presents a new method for trust region subproblems- Tangent Single Dogleg method, this method is proved by analysis and calculated results to be hotter than Powell's single dogleg method.

In this paper, we present a stable numerical algorithm to construct a Jacobi matrix fromthe given spectral data. We first construct a matrix with the given spectral data. Then wetransform the matrix into a Jacobi matrix by using Givens transformations leaving invariantthe given spectral data.

In this paper, a fast grouping and sorting method is given. For given digitaldataX1, X2,…,XN,the total computing amount for sorting data xi into x(1)≤x(2)≤…≤x(N) isin direct proportion to N. Among the 5-sorting methods, it is the best. Compara-tive results from sorting the given data on the computer IBM 4341 are given.

The simulation on a distributed parallel computer system requires parallel ran- dom number generators. In this paper, four algorithms of parallel random number generators are introduced. They are segmented parallel algorithm and leapfrog par- allel algorithm of multiplicative congruential generator and generalized feedback shift register (GFSR) generator, parallel algorithm of lagged-Fibonacci generator,and parallel algorithm of combined generator.

In this paper, we review some recent developments on the study of implicitly defined curves and surfaces in the field of computer aided geometric design(CAGD), includ-ing mainly the research on the problems of parametrization, regularity and splines of algebraic curves and surfaces.

This paper considers the following problem: How to construct a Jacobian matrix from its spectrum and a submatrix. A new numerical method is given.

Voronoi diagrams for general figures are ones built from generators, which include geometric diagrams, such as point, segment, arc, and so on. It was focused herein on Voronoi diagrams for general figures and approximation Voronoi diagrams approximation by approximation structuring. It was proposed that the area surrounded by Voronoi edges, for corresponding to the degree of approximation. Analysis for the factor of the degree of approximation was undergone, using two-point approximation segment and two-point approximation arc. The principle of approximation structuring was at last provided.

Firstly, with the discusses of main ingredients to exert the peak float performance for currently high performance mirco-processors in detail, this paper analyzed the principal motivations for the speedup of parallel applied codes under the parallel computers consisted of the these micro-processors. Secondly, this paper presented a suite of performance evaluations rules for parallel codes, which can reveal the overall numerical and parallel performance with respect to the serial codes, pose the performance improving strategies, explain exactly the reasons for super-linear Speedup. The numerical experimential results of two realistic applied codes under two parallel computer are also given in this paper.

This paper gives the affine invariant Convergence theorm concerning differentialcontinuation and Newton iterative proccesses, it also gives the formulae of optimalefficiency of differential-continuation. These formulae are more efficient than someother methods. Last, some numerical exemples are given.

This paper gives the numerical solutions of two kinds of harmonic canonical integral equations over sector with crack and concave angle, together with their error estimates. Since the Poisson integral formula expresses exactly the singularity, canonical boundary element method has not the shortcoming, due to which the accuracy of general FEM will be lowered seriously in the neighbourhood of singular point.

Ray tracing is a basic aspect in tomography. To solve the caustic problem in inhomogeneous media using Maslov asymptotic theory, we need to calculate the position and slowness vector at every point. Therefore, ray tracing must rely on the ray equations in Hamiltonian form. In this paper, fourth order symplectic scheme and nonsymplectic Runge-Kutta scheme are compared in ray tracing for sinusoidal velocity model. The result indicates that ray paths obtained by two schemes are almost the same. But on keeping Hamilton quantities, the symplectic scheme is far better than the Runge-Kutta scheme. On computing travel time for Htamiltonian system with T parameter, we use trapezoid formula for numerical integration. The result coincides with that obtained using Hamiltonian system with t parameter.

Newton-GMRES method is one of the efficient methods for solving large sparse systems of nonlinear equations. Based on Newton-GMRES method, we can derive the Newton-GMRES with backtracking (NGB) method which is of global convergence property. We focus on in-depth investigation about how to improve the robustness of the NGB method, present two global strategies for further improving the NGB method, and correspondingly, we obtain two globally convergent Newton-GMRES method with strong robustness.