In this paper, some simple determinate conditions for nonsingular H-matrices areobtained, and some results include and generalize the related results in [1, 2, 3].

In this paper a finite element method based on cubic B-spline is presented to obtainnig approximate solution for the equilibrium problems of elastic composite structures on regular regions.A computational scheme well suited for various types of boundary conditions is derived.It is easily carried out by a computer.In comparison with the usual nodal finite element method, the main features of the present method are higher accuracy and more economy in computing storage and time requirements.The effect of imposing natural boundary condition as constraints is considered and it is shown by a plate bending problem that this effect is quite superficial.Several numerical results are presented.

A=(a_ij) ∈R~(n×n ) is termed bisymmetric matrix if We denote the set of all n × n bisymmetric matrices by BSR~(n×n ) In this paper, we discuss the following two problems: Problem I. Given X, Find such that Problem Ⅱ. Gived . Find such that where ||·|| is Frobenius norm, and S_E is the solution set of Problem I. The general form of S_E has been given. The necessary and sufficient conditions have been studied for the special cases AX = B and AX = XA of problem I. For problem Ⅱ the expression of the solution has been provided.

In this paper, several practical sufficient conditions for nonsingular H-matrices are obtained by comparing the elements of a matrix. Advantage of results obtained is illustrated by a numerical example.

The following two kinds of inverse eigenvalue problems arising from structuraldesign are discussed. Problem SIELS: Given a real n×k matrix X_1 (1≤k

This paper, considers the following two problems: Problem Ⅰ. Given X, B R~(n×m),find A∈P_u such that AX = B,where P_u = {A∈R~(n×m)|A=A~x, x~TAx≥0,?x∈R~u}. Problem Ⅱ. Given A∈R~n×n, find A∈S_E such that‖A-A‖ - inf‖A - A‖,where ‖·‖ is Frobenius norm, and S_E denotes the solution set of problem Ⅰ. The necessary and sufficient condition, under which S_E is nonempty, is studied.The general form of S_E is given. For problem Ⅱ, the expression of the solution isprovided.

A new method of constructing stiffness matrices is presented. The method uses two setsof parameters, one of which consists of usual nodal parameters, like function values and theirderivatives at nodes of elements. The second set may be chosen some special type of linear func-tionals on the given finite element spece, such as integrals of functions and their derivativesalong edges of elements in order to meet certain convergence requirements. The method is very effective and easy to implement under the general framework offinite element analysis. Several unconventional plate elements, recently appeared in engineeringapplications, have been tested successfully using this new method and their convergence proper-ties are established in a unified mathematical way.

This paper is devoted to the stability analysis of both the true solution and the numerical approximations for nonlinear systems of neutral delay differential equa-tions(NDDEs) of the general form y'(t) = F(t, y(t), y(t-r(t)), y'(t-r(t))). We first present a sufficient condition on the stability and asymptotic stability of theoretical solution for the nonlinear systems. This work extends the results recently obtained by A.Bellen et al. for the form y'(t) = F(t,y(t),G(t,y(t-T(t)),y'(t-T(t)))). Then numerical stability of Runge-Kutta methods for the systems of neutral delay differential equations is also investigated. Several numerical tests listed at the end of this paper to confirm the above theoretical results.

Tikhonov regularization is one of the most important regularization methods for the study of ill-posed problems.But because of the saturation effect of this method it is impossible that the convergence rate can be improved with increasing smoothness assumption of solution,i.e.,the error estimate between the exact and approximate solutions can not be order optimal.The iterated Tikhonov regulariza- tion prevent saturation effects,such that for any smoothness asumption the error estimate can always be order optimal for appropriate choice of iterated times.

Miscible displacement of one compressible fluid by another in a porous medium is mo-deled by a nonlinear coupled system of two partial differential equations. Two finite elementprocedures are introduced to approximate the concentration of one of the fluids and the pres-sure of the mixture. The concentration is treated by a combination of a Galerkin method andthe method of characteristics in both procedures, while the pressure is treated hy either a Ga-lerkin method or by a parabolic mixed fini~+e element method. Optimal convergence rates in H'are demonstrated for these schemes. Time stepping along the characteristics of the hyperbolicpart of the concentration equation is shown to result in smaller time-truncation errors thanthose of standard methods, Numercal results published elsewhere have confirmed that largertime steps are appropriate with these schemes, and that the approximaxions exhibit improvedqualitative behavior.

In this paper, a new unconventional Hermite-type rectangular element for the second order elliptic problem is constructed. The anisotropic character is proved by using anisotropic interpolate basic theorem, thus this element can be applied to arbitrary rectangular subdivision. At the same time, the superclose and super-convergence properties and extrapolation are obtained, which are independent of the regular assumption and quasi-uniform assumption of the meshes. Numerical results which coincide with our theoretical analysis show that this element indeed has very good convergence behavior.

The purpose of the present paper is to find affine intrinsic invariants of aplane Bezier curve B_n of nth order, and then to give certain geometrical interpretations forthe necessary and sufficient Conditions in order that a plane B_3 should be convex. Further,the inflexion points of a plane B_4 are disscussed with some concreteexamples.

This paper presents a maximum entropy method for solving minimax problemswith inequality constraints, in which a multi-constrained minimax problem is appro-ximated by a differentiable one with a single constraint. An augmented Lagrangianalgorithm is used to solve the resulting problem. Numerical examples are given toshow the high efficiency of the method.

A = (aij) R~n×n is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSR~(n×n) Let Where when n =2k, and n = 2k+1, In this paper, we discuss the following two problems: Problem Ⅰ. Given X R~n×m, B R~n×m. Find A S such that Problem Ⅱ. Given A* E R~n×n. Find A S_E such that Where is Frobenius norm, and S_E is the solution set of Problem I. In this paper the general representation of S_E has been given. The necessary and sufficient conditons have been presented for Problem I_0. For Problem Ⅱ the expression of the solution has been provided.

Let P∈ Rn×n such that PT = P, P-1 = PT.A∈Rn×n is termed symmetric orthogonal symmetric matrix ifAT = A, (PA)T = PA.We denote the set of all n × n symmetric orthogonal symmetric matrices byThis paper discuss the following two problems:Problem I. Given X ∈ Rn×m, A = diag(λ1,λ 2, ... ,λ m). Find A SRnxnP such thatAX =XAProblem II. Given A ∈ Rnδn. Find A SE such thatwhere SE is the solution set of Problem I, ||·|| is the Frobenius norm. In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. The expression of the solution A* of Problem II is presented. We have proved that some results of Reference [3] are the special cases of this paper.

In this paper, we propose a mixed conjugate gradient method for unconstrained optimization based on Hestenes-stiefel Algorithms and Dai-Yuan Algorithms, which has taken the advantages of two Algorithms. We prove it can ensure the convergence under the Wolfe line search and without the descent condition. Numerical experiments show that the algorithm is efficient by comparing with HS conjugate gradient methods and PR conjugate gradient methods.

This paper gives a best operator of interpolation for ball U = {‖u‖≤ρ}inW_2~1[a, b]:H_n~U(x)=sum from j=1 to n(Φ_j(x)f_j),where

Abstract Trust region algorithms for nonlinear optimization and their convergence propertiesare discussed. Convergence results and techniques for convergence analysis are studied.An A (δ,η) descent trial step is defined, and is used to obtain a unified proof for globalconvergence of trust region algorithms

 

This paper describes evolution strategy procedures for real-valued function optimization for the purpose of analyzing its asymptotic convergence properties. Two convergence theorems, which show that evolution strategy asymptotically converges to a global minmize point with probability one, are given.

We study the Hermitian positive definite solutions of the matrix equation X + A*X-qA = I with q > 0. Some properties of the solutions and the basic fixed point iterations for the equation are also discussed in some detail. Some of results in [Linear Algebra Appl., 279 (1998), 303-316], [Linear Algebra Appl, 326 (2001), 27-44] and [Linear Algebra Appl. 372 (2003), 295-304] are extended.

A new type of computable scheme is provided for a class of elliptic bounaryvalue problems with small periodic coefficients. The principle idea of this methodis to change the computation of original problems into the solving process of theperiodic solution defined in the basic condguration and boundary layer. In thispaper, a completely rigorous mathematical theory for this process is presented.

In this paper, a high accuracy differencing scheme with parameterfor solving the parabolic partial differential equation?u/?t= ?~2u/?x~2, 0< x < π, t > 0 (2)is established. While these parameters are chosen as ξ_0 = 5/6, ξ_1 = 1/6, η_0 = 1/2, η_1 = 1/2,the differencing scheme (1) can be written as: The order of the discretization error is, 0(△t~2) + 0(△x~4). Then the absolute stability of thisscheme is proved by means of computing the eigenvalues of a matrix. While the parameters ξ_0 = 5/6, ξ_1 = 1/6, η_0 = 2/3, η_1 = 1/3, are taken, the differencingscheme (1) can be written.The order of the discretization error 0(△t~4) + 0(△x~4) may be reached. But it is very interestingthat the implicit differencing scheme, which has a very high accuracy, is absolute instability.

In this paper, we first defind the connective diagonally dominant matrix. Then we dis-cuss its some properties.

A∈Rn×n is called a bisymmetric matrix if A = (aij)n×n,aij = aji,a,ij = an+1-i,n+1-j(i, j = 1)2,…,n). The set of all n×n bisymmetric matrices is denoted by BSRn×n. By using Moore-Penrose generalized inverse and the Kronecker product of matrices, we derive the expression of the least squares symmetric solution of the matrix equation AXB + CYD = E with the least norm. Based on this, we present the expression of the least squares bisymmetric solution of the matrix equation AXB = C with the least norm, and provide a numerical algorithm and numerical experiments for finding the least squares bisymmetric solution with the least norm.

In this paper, a nonconforming element like Wilson's for second order proble-ms is proposed, which satisfies the patch test for arbitrary quadrilateral meshes.

Let S={A∈SIR~(n×n)|f1(A) =||AX1-B1||= min}, where X_1, B_1 ∈IR~(n×k)_1) SIR~(n×n)= {A∈IR~(n×n)|A~T= A},||.||.is the Frobenius norm. We consider the following problems: Problem Ⅰ. Given X_2, B_2 ∈IR~(n×k)_2, find A ∈ S such that f_2(A) = ||AX_2-B_2||= min. Problem Ⅱ. Given A ∈IR~(n×n), find A∈S_A such that ||A- A||=inf||A-A|| where S_A is the solution set of Problem Ⅰ. The general form of the solution set S_A of Problem Ⅰ is given. The expression of the solution A of Problem Ⅱ is presented. The numerical method is described and numerical experiments are included. Many available results are subsumed under those presented in this paper.

Under the assumption that the function is analytic, Smale presents a wellknown criterion α which is used to study the behaviours of the convergence of Newton's method for finding zeros of a function and establishes a complete theory.In this paper we reestablish the whole theory of Smale's in the assumption that the function is the second continuously differeatiable.

A three level explicit difference scheme for solving parabolic equations is pro-posed. Tbe stability condition and local truncation error for the scheme are r<1/2 and O(△t~2)+O(△x~4),respectively.

This paper extends the difference schemes for the simple wave equation to those forthe dispersive equation.

Abstract In this paper two explicit difference Schemes U_m~(n+1) = r(U_(m+1)~n - U_(m-3)~n) + (1-2r)(U_m~n - U_(m-2)~n) + U_(m-2)~(n-1) α>0,and U_m~(n+1) = r(U_(m+3)~n - U_(m-1)~n) + (1 + 2r)(U_m~n - U_(m+2)~n) + U_(m+2)~(n-1), α<0,where r = ατ/h~3(τ = Δt, h = Δx), for solving the dispersive equation u_t = au_(xxx) areestablished. The local truncation errors and stability condition for the two schemes are O(τ + h~2)and |r|≤0.7016, respectively.

The concept of α-connective diagonal dominance for matrices are introduced, and new conditions for H-matrices are obtained.

In this paper, we shall discuss the homogenization problem of boundary value problems for the systems of linear elasticity with the quasi-periodic microstruc-tures, and give several basic estimations for displacement,stress and strain en-ergy,which are the basis of finite element computing.

Nonsingular H-matrices play a very important role in many fields,but it is difficult to determine a nonsingular H-matrix in practice.In this paper,we gave one type of new criteria conditions for nonsingular H-matrices,and improve some relate results.Advantages are illustrated by numerical examples.

Two methods of approximation, circular arcs and biarc curve approximation, aredescribed. The error analysis of these methods are given. The applications of thesetwo methods to numerical computation and geometric design are discussed.

In this paper, a finite difference-streamline diffusion finite element scheme for time-dependent nonlinear convection-dominated diffusion problem is constructedand a quasi-optimal order error estimate in L2-norm is derived.

An economical difference scheme is proposed to solve convection-diffusion equations. The transport term is discretized by the method of characteristics, then the difference system are docomposed to several problems of individual variable using alternating direction method. Two kinds of interpolation operators are supplied for the technique of characteristics. The stability and convergence are analysed by energy method. Numerical result implies that this scheme has better accuracy and higher efficiency then the standard scheme of two-order center difference quotient.

In this paper a new domain decomposition method is suggested and its convergence is proved. This method is based on the natural boundary reduction and suitable for solving some elliptic boundary value problems over unbounded domain.The finite element method and the natural boundary reduction are alternatively applied to a bounded subdomain and a typical unbounded subdomain. It has overcame the difficulty met in standard domain decomposition method and has many advantages. Moreover, especially for the exterior circular domain, an estimate for contraction factor is given.

Stability and error estimates are established for the finite element method to solvea class of second oder nonlinear hyperbolic equations. Optimal rates of convergencefor the continuous time and the discrete time are established as well.

The authors provide two methods for fitting one-dimensional data points in com-puter aided geometric design: to fit the given data points with the least squares of theBezier curve or cubic B-spline curve. To obtain the fair B-spline curve and to controlthe fairing and deviation, a fair weighted term is introduced.