In this papert the routing problem in virtual circuit networks is considered. We consider the problem of choosing a path for each origin-destination pair to minimize the average delay encountered by packts. We give the usual formulation of this problem as a nonlinear combinatorial optimization problem. We present a genetic algorithm to solve this problem. Extensive computational results across a variety of networks are reported. These results indicate that our method outperforms the other methods in the literature.

In the exact nonparametric illference, we frequelltly need the enumeration of all contingency tables with the same marginal totals. A qualltum jump toward a more rapid method took place with the publication of the network approach of Mehta et al.[1-3]. It circumvents the need to explicitly enumerate each table and considerably extends the bounds of computational feasibility relative to the direct enumeration. In this paper) the present authors suggest another algorithm of implicit enumeration of all tables. First, a contingency table (T × c table or stratified 2×c table) is regarded as a number with several digits, and all contingency tables with the same marginal totals are regarded as a number sequence. A rule is then intyoduced to generate the sequence and to leap some subsequences which are useless for computing the probability values. The leaping subsequence aIgorithm proposed is more efficient than the network algorithm. Especially, when-the permutation distribution is required, our algorithm may run tens times faster than StatXact.[4]

In this paper a new algorithm of B-spline curves with given tangnt polygons is discribed. In the algorithm the all de Boor points of the B-spline curves can be cal culated simply by the vertices of the given tangellt polygons. The constructed curves are shape-preserving to tangent polygons. The local modilications for thes curves are possible. At last several examples are given.

In this paper, the serial algorithm analysis and parallel implementation of generalized eigenproblem of synuntric matrices are considered. meanwhile, the complexity of algorithm is analyzed. The computational results about speed up are done on Dawning 1000 parallel computer.

In this paper, we construct a hybrid evolutionary strategies (HES) for constrained optimization problems. Evolutionary strategies (ES) and hybrid evolutionary strategies (HES) are comparied on two constrained problems. Theoretical analysis and experimental data show that the HES has high converge speed and stability It can be applied in many constrained optimization problems in engineering practically.

The double circle-arc fitting in the same direction and in the opposite direction are given in the original coordinates for arbitrary plane parametric curves, after the straight line, the circular-arc, the parametric curve and its tangent line are oriented. The circular-arc fittings for plane curve of tabular points are discribed by using the cubic spline function. Newton method is used to calculate the maximum error and the result of high precision has been gained by densifying points. The advantage of the method is that if overcomes difficulties of large defiection, high precision, huge programming, and avoid solving the nonlinear equations.

Do-loop unrolling is an effective technique for improving performance of applicistion programs. This paper presents a method for unrolling nested Fortran DO-loops using the m4 macro language. m4 is a macro processor widely available on UNIX platforms. By using carefully designed m4 macros, Do-loop unrolling becomes much simpler. More over, with this method, code can be written for general ullrolling parameters, allowing the program to be easily tuned bn different computers to reach optimal performance.

In this paper, based on the natural boundary reduction suggested by Feng and Yu,an overlapping domain decomposition method for harmonic boundary value problerns on the unbounded sector domain or the unbounded cracked domain is discussed. The numerical examples show that this discrete Schwarz iteration is geometric convergent.And the convergence rate of this method is independent of the finite element mesh size,but dependent on the frequency of the exact solution and the overlaPping degree of thesubdomains.

A new algorithm, based on the combination of the evolutionary programming and the classical gradient adustment techniques. Its efficiency is higher than that of general evolutionary programming. Numerical results demonstr8te the validity and effectiveness.

This paper presents an infinite element in the finite e1ement method of lines (FEMOL).The line mapping technique is used to map infinite lines to a standard local interval.The gain from this mapping is twofold: on the one hand, it standardizes the definition intervals; on the other hand, it changes the solution property in the local space so that the solution can be sought in a polynomial space with the conditions at the infinity automatically satisfied. The proposed approach is simple and efficient. With the solutions on infinite lines are obtained by solving governing ordinary differelltial equations,the overall solution is highly analytic and accurate. Some typical numerical examples are given in the paper to demonstrate the remarkable performance of the proposed method.

In this paper, a new method is presented for fairing B-spline curves with fixed area constraints. Authors use Lagrange's method of multipliers solved the variational problem with constraints.

Levenb erg-M arquardt method was first suggested by Levenberg and Marquardt in the context of nonlinear least sqares. This paper will develop a Levenberg-Marquardt method for semidefinite programming, which is global collvergence and easy to implement. Some promising numerical results are also contained.

In this paper an interval verification algorithm for the solutions of nonlinear systems is presented. The algorithm combines the high convergent speed of the floating-point iterative methods and the rigorous inclusion property of the interval methods. By using the so-called epsilon-inflation, .the algorithm might be reliably used to solve various nonlinear systems, and the sufficiently rigorous error bounds of the solution could also be produced.Besides, a verification algorithm given by G. Mayer is also discussed. A Mayer's open question is answered negatively by constructing a simple counterexample, and a new conjecture about this algorithm is presented by the author.

In using the methods given by [1] to compute the hypersingular integrals on interval,one should select the mesh carefully in such a way that singular point falls near the center of a subinterval. A numerical method given in this paper might solve this problem. This new method is very simple, easy to be implemented, and above all, notaffected by the location of singular point.

In this paper, we present a simplified third-order weighted ENO finite volume method on unstructured triangular mesh. The third-order TVD Runge-Kutta time diswcretization is used. A weighted quadratic reconstruction is constructed on every triangular mesh. Preliminary encouraging numerical experiment is given.

Parallel multigrid computations for high Reynolds Steady-state incompressible enterring flows and recirculating flows Navier-Stokes equations are organized in this paper.Based on the existed successful serial algorithms, combined with the typical numerical examples, we carefully analyzed the decrements of numerical convergence rates and the increaments of parallel efficiencies owing to the introductions of Schwarz parallelizations suitable for grid partitioning to obtain large granularity parallelism. Detail parallel numerical performence results are

The explicit formulation of the surrogate dual of quadratic programming is given in this paper, and the condition on which no gap will occur between the primal and the dual is found by using Karush-Kuhn-Tucker conditions. Karmarkar ' s algorithm is used to solve the surrogate dual problem. Numerical examples show the algorithm proposed robust and stable.

This paper describes the work on parallelization of the tracer interfaces moving grid method program, and gives some numerical experiments on several computers.

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.

With three unfixed parameters (m, a, b), the nonlinear regression model, y = m -exp(ax+b+), is considered traditionally to be out of solution by using linear conversionway. Depending on linear regression and iteration way, this paper presents a new wayto solve this problem.

A sequence of pseudorandom numbers with fine properties is of great significancefor random simulation. In this paper we discuss properties of the combined sequencefrom the angles of period, two-dimensional and probabilitical structure, and point outthat under certain condition a combined sequence is much more superior to any of itscomponents. In addition, we give digital examples for comparison.

The mathematical model, which describes the contamination process between batchesin multi-medium pipeline transport under turbulent flow, is the diffusion-covectionequations. These equations for laminary bottom layer, buffer layer and turbulent coreare seperated into net convection equations and net diffusion equations, which aresolved respectively by characteristic method and implicit difference method to obtainnumerical solution. The results of the numerical study explain the forming and de-veloping process of contamination much better, and also account for the phenomenonof non-symmetrical mean concentration distribution of contaminant between batches,which can not be explained by other analytical method.

A predictor-correct interior point method is presented for solving convex quadraticprogramming problem with box constraints in this paper. Actually, the method isequivalent to solve a system of equations-the first order optimality conditions of theproblem by decomposing one Newton step with one simplified Newton step, and hasa nice convergent property with high order. Moreover, the center direction generatedby introducing the barrier parameter is used to correct the descent Newton directionsuch that the search direction which consists of the center and Newton direction avoidshitting the board of the feasible region. Therefore, the iterative sequence generated bythe algorithm is remained inside of the feasible region and converges to the optimalsolution. The numerical results for a group of test problems are also given, and haveshown that the algorithm works very efficiently.

A finite volume program for the calculation of plane cascade flow at large angle-of-attack is developed. The Osher- Chakravarthy 3rd order TVD scheme is used toensure the high accuracy, and the technique of diagonalization is adopted to fast theconvergence speed. Two kinds of non-reflective boundary conditions are explored atthe inlet and outlet boundaries, which can reduce the scale of computational domainand avoid too many grid points for simulations of flow separation and shock waves.

Based on the interval analysis, a practical interval algorithm is developed for findingall global minimizers of a nonsmooth function on a closed domain, which is given bydefining a special derivative to the function and using the ifiterval inclusion of derivative.Both theoretical analysis and numerical results show that this method is practical andeffective.

This paper presents a divide and conquer algorithm for solving the eigenvalue prob-lem of real symmetric band matrices. The new algorithm bases on homotopy con-tinuation, including inverse power iteration and inverse subspace iteration with shift.Numerical results show that our algorithm is strongly competitive with the known algo-rithms in speed. Above all, our algorithm is well suitable for parallel implementation.Numerical results of parallel computing are also presented in this paper.

In this paper, we introduce the methods and techniques on how to improve the.efficiency of BLAS on Hitachi SR2201, and with some exapmles we evaluate and analyzethe Speed up version BLAS.

A new multipoint scheme method is given for a kind of nonlinear evolution equation in this paper. Numerical experiments of KdV and MKdV equations are done by the new method. The results are compared with those of other numerical methods, and some graphical representations of the solitons are provided. It is proved numerically that the method is better than the other methods.

A multispecies, multispeed lattice Boltzmann model is presented to study the mass diffusion properties. At each node the total momentum of all particles and the partial masses of the particles of same species are conserved. Using the Chapman-Enskog method, we have derived from the BGK Boltzmann equation the N-S equation and partial mass conservation equations. We have compared the measured diffusivities with the theoretical values for different single relaxation time, showing good agreemellt. We have carried out the 2-D convection-diffusion simulations on a 16o × 100 hexagonal lattice. At the initial time we inject a bubble of radius r(= l6 nodes), at rest, filled with particles of one species into a uniform flow of particles of the other species. The mean velocity v = 0.5 is along the horizontal axis. One clearly observes the deformation and the diffusion of the bubble.

In this pa[er, we give a faSt algorithm to compute inverse of r-circulan matrixand symmetric r-circulat matris, when circulaat matrir is nonsingular; to computethe group inverse of r-circulant matris, when r-circulant marix singufor; to computethe {1, 2} inverse of symmetric r-circulant matris, when symmetric r-circulant matrix singular.

In iolving the regression equations, collinearity in the design matrix can result in Paraznter estimates which are inaccurate. The use of orthogonal matris transformatha such as the singubovalue decomposition can reduce the effect of collinearity Also, estAnates of the regression coefficients can sometimes be improved through the Process known as iterative refinement. The application of iterative refinement to the singular-value decomposition solution of the regression equations is described. Results show that iterative refinement using the singular-value decomposition can improve res gression coefficient estimates, in cases where the design matrir is highly collinear.

In this paper, superparametric discontinuous boundary elements are developed to discretise boundary iotegral equation of three-dimensional Laplace equation and Helmholtz equation. Quadratic polar coordinate transformation is employed to evaluate the singular integraIs. It is illustrated that the associated strongly singular integrals cax be obtained directly

In this paper we present a method for solving linear programming. The main idea is that, if we have gotten an optimal solution of the linear progranuning min s = c x.subject to Az = b,x＞0,with simplex method, we can easyly get a solution of the linear progranunin We call the method an orderadding method.

A new matrir Pade approximants (GMPA) based on generalized inverse was at first introduced by [1]. The aim of this paper is to give a Psaan formula for denominator polynomial of GMPA, which should represent the denominator more accurately than the standard determinantal form in [1]. The result derive from Cayley theorem [6] which states that the determinant of a bordered zero-axial skew-symmetric matrix is the product of two Pfaffians. As a important result, the Pfaffian formula of denominator polynomial of type [4/4] for CMPA is established and ls applied to approximate matrix exponential functions.

In this paper, the hydrodyntalc calculation is assumed to be split into two phase.The first phases is a Lagrangian phase, in which the Lagrangiau equations in conservative form are integrated by Flux-Corrected transport (FCT) mehod, and all state variables are cellcentered. The second phase is referred to as the advection Phase or the remapping phase, and it accounts for the transport of material between the Eulerian cells. The methods are examined numrically with two 2-D shoch rbofon problms.The results show that they are successful.

In this paper we discuss problems concerning the structure of L-combined sequence {Zn, n∈ N}. By showing that all points of z. (k) lie in a group of (k - 1)-dimentional parallel hyperplanes in Dk, we point out that under quite general conditions {Zn, n∈N} is much superiorer to its combined sequences and thus can be used to improve the effect of stochastic shalation. In addition, we also give digital exarnples to demonstrate the effect on simulation by using {Zn, n ∈ N}.

In this paper I will discuss the properties of the. stochastic webs through computation. For a kind of generdsedly seperable Hamiltonian system Iprove a kind of corresponding explicit symplectic scheme, and prare that the altnding explicit schemes are of second order. This was fiot proped by professor Feng Kang[18,19]. I apply this kind of schemes to the one-dimensional genealindly operthe Hamiltonian system, and obtain stochastic webs.