中国科学院数学与系统科学研究院期刊网

计算数学 1998年 20卷

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1. C~k连续的保形分段2k次多项式插值
方逵,朱国庆,罗建书
计算数学    1998, 20 (1): 1-10.   DOI: 10.12286/jssx.1998.1.1
摘要1314)      PDF(pc) (338KB)(852)    收藏
This paper describes a method for shape preserving smooth piecewise polynomial S(x) of degree 2k which passes through a given set of data points {x1, yi}i=0 n+1 (xi<xi+1 , i =1, 2,…, n + 1). If we give the first derivative of curve at each data point, then in data interval [xi, xi+1] a necessary and sufficient conditions is derived for the convexity preserving of interpolation polynomial of degree 2k. By inserting at most one internal knot at each data interval, a Ck shape preserving piecewise interpolating polynomial of Degree 2k is obtaind. At fat a few data examples illustrate the method is correct and effective.
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2. 无界区域上基于自然边界归化的一种重叠型区域分解法及其离散化
郑权
计算数学    1998, 20 (1): 11-24.   DOI: 10.12286/jssx.1998.1.11
摘要1704)      PDF(pc) (568KB)(598)    收藏
In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is discussed. This method is very effective especially for problems over unbounded domains. The geometric convergency of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show that the convergence rate of this discrete Schwarz iteration is independent of the finite element mesh size, but dependent on the frequency of the exact solution and the overlapping degree of the subdomains.
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被引次数: Baidu(58) CSCD(6)
3. 对凝聚函数法的探讨
杨庆之
计算数学    1998, 20 (1): 25-34.   DOI: 10.12286/jssx.1998.1.25
摘要1139)      PDF(pc) (360KB)(641)    收藏
In this paper, first the convergence of the coherent function method is given.Then we discuss the error of solutions for detail. The best and "almost" best error bounds are obtained. Finally we examine some numerical examples by using previous theoretical resalts.
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被引次数: CSCD(11)
4. 一阶双曲问题的间断流线扩散法
孙澈,汤怀民,吴克俭
计算数学    1998, 20 (1): 35-44.   DOI: 10.12286/jssx.1998.1.35
摘要1349)      PDF(pc) (377KB)(721)    收藏
In this paper, a new finite element method, discontinuous-streamline diffusion method, is studied for first-order linear hyperbolic equation. A discontinuity-type explicit finite element scheme with artificial diffusion parameter is constructed, the stability and optimal rate of convergence in proper norm are established for the considered scheme. Finally, a numerical example is provided to show the highly efficiency of the now scheme.
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被引次数: Baidu(26)
5. γ-循环线性方程组的快速算法
成礼智
计算数学    1998, 20 (1): 45-55.   DOI: 10.12286/jssx.1998.1.45
摘要1175)      PDF(pc) (391KB)(655)    收藏
The fast Hartley transform (FHT) and fast W transform (FWT) algorithm for,solving welLconditioned r-circulant equations is presented in this paper. The arithmetic operation save about half compared with the fast Fourier transform (FFT) algorithm. For ill-condotioned cases, an efficient numerical stable methods for solving r-circulant equations is suggested by using FHT, FWT and truncated singualr value decomposition (TSVD) method. An open problem is solved.
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被引次数: Baidu(8)
6. 关于“交错网格紧致差分格式和满足等价性的压力Poisson方程”一文的两点说明
于欣
计算数学    1998, 20 (1): 56-57.   DOI: 10.12286/jssx.1998.1.56
摘要1035)      PDF(pc) (392KB)(989)    收藏
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7. 解非线性方程组的一类离散的Newton算法
陈志,高旅端,邓乃扬
计算数学    1998, 20 (1): 57-68.   DOI: 10.12286/jssx.1998.1.57
摘要2225)      收藏

This paper discusses a class of discretized Newton methods for solving systems of nonlinear equations. The number of function evaluations requred by the new discretized algorithm is about half of the classical discretized Newton method as Brown and Brent methods. The approximation given by the algorithms to F'(x) is strongly consistent. The algorithms can reduce to the Newton method when the difference stepsize h approaches to zeros but Brown and Brent methods can't do it. Numerical results show the algorithms are efficient.

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被引次数: Baidu(19) CSCD(2)
8. 非定常的热传导──对流问题的混合有限元法
罗振东
计算数学    1998, 20 (1): 69-88.   DOI: 10.12286/jssx.1998.1.69
摘要1405)      PDF(pc) (726KB)(762)    收藏
In this paper we have studied the mixed finite element method for the non stationary conduct ic n-convection problems, where the coupled equations governing viscous incompressible flow and heat transfer process, and incompressible fluid are the Boussinesq approximations to the nonstationary Navier-Stokes equations.We have discussed the existence of continuous, semi-discrete and fully discrete solutions, and derive the error estimates for the approximate solutions on the continuous and discrete time cases.
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9. 基于双尺度渐近分析的有限元算法
崔俊芝,曹礼群
计算数学    1998, 20 (1): 89-2.   DOI: 10.12286/jssx.1998.1.89
摘要1145)      PDF(pc) (464KB)(838)    收藏
The finite element computing methods and the error estimations based on twoscale asymptotic analysis method (see [1]) are presented. Finally, numerical results are given for a typical model. A variety of numerical experiments show the capabilities and reliablity of the proposed method.
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被引次数: Baidu(42) CSCD(12)
10. 声波方程吸收边界条件的稳定性分析
张关泉,魏素花
计算数学    1998, 20 (1): 103-112.   DOI: 10.12286/jssx.1998.1.103
摘要1119)      PDF(pc) (334KB)(782)    收藏
In this paper we present a set of absorbing boundary conditions based on the higher order approximations of one-way wave equations. By introducing new functions, these absorbing boundary conditions are put into the form of systems of lower order partial differential equations. The stability of initial boundary value problems with these type of boundary conditions is discussed. The energy estimates for their solutions are obtained.
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被引次数: Baidu(15) CSCD(1)
11. 无约束非光滑优化问题的信赖域算法及收敛性
刘国山
计算数学    1998, 20 (2): 113-.   DOI: 10.12286/jssx.1998.2.113
摘要1242)      PDF(pc) (166KB)(1045)    收藏

1.引言考虑下列无约束非光滑优化问题:其中f为R”上的局部LIPSChitZ函数.本文将11·112简记为11·l.信赖域算法是通过求解一系列子问题3*B(二,凸):来求解问题(1)的,其中拉x,·)为j在x点的一阶近似,B为nxn阶对称阵.下面给出信赖域的基本算法TRA:步1·给定...

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被引次数: Baidu(28) CSCD(4)
12. 一种二次保形插值参数曲面
王艳春
计算数学    1998, 20 (2): 121-.   DOI: 10.12286/jssx.1998.2.121
摘要1595)      PDF(pc) (303KB)(1391)    收藏

A shape preserving surface interpolation scheme to data set without three consecutive collinear data points in both x and y directions is presented, which is a piecewise quadratic parametric polynomials, and is G1 or C1 continuous as desired on the whole domain. The interpolating surface can preserve the convexity, concavity, inflection property and monotonicity of the data set. Futhermore, some parameters (such as the cross boundary tangent vectors of the adjacent sub-surfaces) can be freely chosen within a certain extent to adjust the shape of the interpolating surface or to obtain a better approximation to the original function from which the data come. The shape preserving interpolation to an arbitrary set of data on rectangular grids is also discussed, and an algorithm with generality is described, a special case of which is the algorithm of the above G1 (or C1) shape preserving interpolant. A number of examples of the algorithmsare given.

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被引次数: Baidu(11)
13. 一类时空二阶精度高分辨率MmB差分格式的构造及数值试验
郑华盛,赵宁,戴嘉尊
计算数学    1998, 20 (2): 137-.   DOI: 10.12286/jssx.1998.2.137
摘要1465)      PDF(pc) (613KB)(1042)    收藏

In this paper, a new Riemann-solver-free class of difference schemes are const ructed to 2-D scalar nonlinear hyperbolic conservation laws. We proved thatthese schemes had second order accurate in space and time, and satisfied MmB properties under the appropriate CFL limitation. Moreover, these schemes hadbeen extended to systems of 2-D conservation laws. Finally, several numericalexperients show that the performance of these schemes are quite satisfactory.

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被引次数: Baidu(25) CSCD(6)
14. 线性流形上的两类矩阵最佳逼近问题
曹建胜
计算数学    1998, 20 (2): 147-.   DOI: 10.12286/jssx.1998.2.147
摘要1213)      PDF(pc) (342KB)(1173)    收藏

The two classes of best approximation of a matrix on the linear manifold are discussed by using the row string operator and the generalized singular value decomposition of a matrix. The solutions of the problems and a numerical method for solving the problems are given. The problems discussed in some papers could be subsumed in the cases proposed in this paper.

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被引次数: Baidu(25) CSCD(5)
15. 并行二级多分裂迭代方法
谷同祥,刘兴平
计算数学    1998, 20 (2): 153-.   DOI: 10.12286/jssx.1998.2.153
摘要1505)      PDF(pc) (225KB)(1067)    收藏

In this paper, we proposed various types of synchronous and asynchronous twostage multisplitting iterative methods for the parallel solution of linear algebraic systems. Convergence theories were given and relaxed forms of these methodswere investigated when the coefficient matrix is either monotone or an H-matrix.Computational experiments on CHALLENGE-L were presented.

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被引次数: Baidu(37) CSCD(7)
16. 板问题三次样条有限元的超收敛及高精度组合公式
舒适,喻海元,黄云清
计算数学    1998, 20 (2): 167-.   DOI: 10.12286/jssx.1998.2.167
摘要1322)      PDF(pc) (537KB)(1151)    收藏

This paper discuss the bicubic spline element solution for plate problem, we obtain the superconvergence result with two order higher than ordinary accuracy,i.e.Moreover, we get the asympototic expansion and superconvergence result of the first and second derivatives. A combination formula of the second derivative which have the accuracy of O(h4) is also derived.

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被引次数: Baidu(3) CSCD(1)
17. 半定规划的近似中心投影法
何炳生
计算数学    1998, 20 (2): 175-.   DOI: 10.12286/jssx.1998.2.175
摘要1317)      PDF(pc) (297KB)(1181)    收藏

Many problems in mathematical programming can be modelled as semidefinite programming. The success of interior point algorithms for large-scale linear programming has prompted researchers to develop these algorithms to the semidefinite programming (SDP) case. In this paper, we extend Roos's projective method for linear programming to SDP. The method is path-following and based on the useof a multiplicative barrier function. The iteration bound depends on the choice ofthe exponent μ in the numerator of the barrier function. The analysis in this paper resembles the one of the approximate center method for linear programming, as proposed by Rocs and Vial [14].

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被引次数: Baidu(14) CSCD(4)
18. 异步并行非线性对称Gauss-Seidel迭代算法
白中治
计算数学    1998, 20 (2): 187-.   DOI: 10.12286/jssx.1998.2.187
摘要1534)      PDF(pc) (427KB)(1207)    收藏

Asynchronous parallel multisplitting nonlinear symmetric Gauss-Seidel methods are established for the system of nonlinear equations , withA, B∈L(Rn) being matrices of particular properties, being diagonal and continuous mappings, and b ∈Rn a known vector. The establishments of these new methods are according to the principle of sufficiently using the delayed information and are concerning about the concrete characteristics of the multiprocessor systems. Therefore, they have considerably higher parallel computingefficiency. The global convergenge as well as the asymptotic convergence rates of these new methods are investigated in detail under suitable conditions.

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19. Lagrangian乘子区域分解法的一类预条件子
胡齐芽,梁国平
计算数学    1998, 20 (2): 201-.   DOI: 10.12286/jssx.1998.2.201
摘要1207)      PDF(pc) (514KB)(1191)    收藏

In this paper we construct a kind of simple preconditioner for non-overlapping domain decomposition methods with Lagrangian multipliers. It will be shown that condition numbed of the preconditioned interface matrix is almost optimal.

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被引次数: Baidu(4) CSCD(3)
20. 非线性对流扩散问题的差分-流线扩散法
张强,孙澈
计算数学    1998, 20 (2): 213-.   DOI: 10.12286/jssx.1998.2.213
摘要1215)      PDF(pc) (334KB)(1269)    收藏

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.

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被引次数: Baidu(101)
21. 非线性波动方程的交替显-隐差分方法
蔚喜军
计算数学    1998, 20 (3): 225-238.   DOI: 10.12286/jssx.1998.3.225
摘要2221)      收藏

A alternating explicit-implicit difference scheme for solving the initial-boundary problem of the nonlinear wave equations at one dimension, two dimensions and three dimensions is given. The convergence of the difference solution is obtained.

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被引次数: Baidu(7) CSCD(1)
22. 惯性算法的收敛性和稳定性
何银年,李开泰,黄艾香
计算数学    1998, 20 (3): 239-250.   DOI: 10.12286/jssx.1998.3.239
摘要1243)      收藏
This paper describes an inertial algorithm of the nonlinear evolutionary equations and prove the boundedness, convergence and stability of this algorithm. Comparison is also made with the usual Galerkin algorithm. Comparison shows that the inertial algorithm is prior to the usual Galerkin algorithm and is a robust and economical computational method.
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23. 求解刚性常微分方程的并行Rosenbrock方法
陈丽容,刘德贵
计算数学    1998, 20 (3): 251-260.   DOI: 10.12286/jssx.1998.3.251
摘要1366)      PDF(pc) (289KB)(841)    收藏
In this paper a class of parallel Rosenbrock Formulas in real-time simulation is constructed for the multiprocessor system. A-stable formulas of two-stage thirdorder and A(α)-stable formulas with α≈87° of three-stage forth-order are constructed. The numerical examples demonstrate that these formulas can solve the initial problems for the stiff ordinary differential equations with high efficiency.
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被引次数: Baidu(64) CSCD(1)
24. 积分算子方程的连续型配置方法
胡齐芽
计算数学    1998, 20 (3): 261-266.   DOI: 10.12286/jssx.1998.3.261
摘要1242)      PDF(pc) (259KB)(769)    收藏
In this paper we discuss the continuous piecewise polynomial spline collocation method for a kind of integral operator equations, which include smooth kernel Fredholm equations and Volterra equations as well as Green's kernel integral equations. It will be shown that the collocation solution itself may admit an ideal error expansion at the knots. Based on this expanison, the multilevel corrected global estimates can be obtained by using the "higher order interpolation" technique.
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25. 关于TLS和LS解的扰动分析
魏木生
计算数学    1998, 20 (3): 267-278.   DOI: 10.12286/jssx.1998.3.267
摘要1336)      PDF(pc) (417KB)(981)    收藏
There are a number of articles discussing perturbation of the total least squares (TLS) and the least squares (LS) problems. In this paper we propose a new orthogonal projection method to improve existing perturbation bounds of the TLS and LS problems.
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被引次数: Baidu(47) CSCD(4)
26. 整周期复合材料弹性结构的有限元计算
曹礼群,崔俊芝
计算数学    1998, 20 (3): 279-290.   DOI: 10.12286/jssx.1998.3.279
摘要1513)      PDF(pc) (419KB)(918)    收藏
Based on the two-scale asymptotic analysis method for elastic structures of composite materials formed by entirely basic configurations, the finite element formulation and its error estimates are presented in this paper. Meanwhile, the approximate formulas of Du are also set up.
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被引次数: Baidu(48) CSCD(1)
27. 用多项式变换计算多维离散W变换
曾泳泓,李晓梅
计算数学    1998, 20 (3): 291-298.   DOI: 10.12286/jssx.1998.3.291
摘要1212)      PDF(pc) (306KB)(773)    收藏
In this paper, the Multi-dimensional Polynomial Transform is used to convert the Multi-dimensional W Transform (MDDWT) into a series of one-dimensional W transform (DWT). Thus, a new polynomial transform algorithms for MDDWT is obtained. The algorithm needs no complex number operations and is simple in structure. The number of multiplications for computing a r-d DWT is only times that of the common used row-column method. The number of additions is also reduced considerablely. Running time of the algorithm on micro-computers is given and is compared with the common used row-column method.
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被引次数: Baidu(1)
28. 摩擦接触问题正则化方法的注记
王烈衡
计算数学    1998, 20 (3): 299-304.   DOI: 10.12286/jssx.1998.3.299
摘要1293)      PDF(pc) (153KB)(847)    收藏
In this note, using precise estimates for the regularized functionals, the upper and lower monotone approximations, in the sense of energy, of the regularized methods for the simplified contact problem with Coulumb friction are presented,and a posteriori error estimate is obtained.
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被引次数: Baidu(16)
29. 非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅰ):时间连续情形
罗振东,王烈衡
计算数学    1998, 20 (3): 305-324.   DOI: 10.12286/jssx.1998.3.305
摘要1188)      PDF(pc) (788KB)(705)    收藏
In this paper, a nonlinear Galerkin (semi-discrete) mixed element method for the non stationary conduction-convection problems is presented. The scheme is based on two finite element spaces XH and Xh for the approximation of the velocity,defined respectively on a coarse grid with grid size H and another fine grid with grid size h << H, a finite element space Mh for the approximation of the pressuxe and two finite element spaces WH and Wh for the approximation of the temperature,also defined respectively on the coarse grid with grid size H and another fine grid with grid size h << H. Both of the non linearity and time dependence are treated only in the coarse space. We have proved that the error between the nonlinear Galerkin mixed element solution and standard Galerkin mixed element solutionis of the order of Hm+1(m>1), all in velocity (H1(Ω)2 norm), pressure (L2(Ω)norm) and temperature (H1 (Ω) norm).
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被引次数: Baidu(58) CSCD(8)
30. 解非定常不可压Navier-Stokes方程的压力修正投影法的并行算法研究
鞠立力,张林波
计算数学    1998, 20 (3): 325-336.   DOI: 10.12286/jssx.1998.3.325
摘要1354)      PDF(pc) (574KB)(882)    收藏
This paper deals with parallel implemeatation on distributed memory systemsof a pressure-correction projection scheme for the unsteady incompressible NavierStokes equations, the CNMT2 scheme (i.e., the Crank-Nickolson Modified Temamscheme Ⅱ), presented in [1, 2]. The key point of this work is to study parallelizationof the fast Poisson solver [2] and analyse its parallel efficiency. Various techniques,such as pipelining and canon cyclic algorithm, were used to ensure good parallel performance and scalability of the algorithm. The algorithm has been implemented using MPI message passing environment and numerical tests have been carried out on various computers, including the home made Dawn-1000 MPP system and workstation clusters.
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被引次数: Baidu(4) CSCD(3)
31. 一类求解单调变分不等式的隐式方法
何炳生
计算数学    1998, 20 (4): 337-344.   DOI: 10.12286/jssx.1998.4.337
摘要1361)      收藏
In this paper we introduce a class of iterative methods for solution of monotone variational inequalities. The method can be viewed as an extension of the Levenberg-Marquardt method for unconstrained optimization, or the generalization of the Douglas-Rachford operator splitting methods when applied to monotone variational inequalities. Each iteration of the method consists essentially of solving a system of nonlinear equations. The convergence proof for the presented method is very simple
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被引次数: Baidu(14) CSCD(2)
32. 一类亚半正定矩阵的左右逆特征值问题
欧阳柏玉
计算数学    1998, 20 (4): 345-352.   DOI: 10.12286/jssx.1998.4.345
摘要1752)      收藏
In 1995 Liao Anping and Guo Zhong in [1] raised a problem that a class of left and right inverse eigenvalue problem for semipositive subdefinite matrices was not touched and wanted to research. In this paper, we will consider this problem.Problem I: given X, Z , Y, W , find A , such that AX=Z,Where The necessary and sufficient conditions for the solvability of this problem are obtained,the expression of the general solution of this problem is also given.
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被引次数: Baidu(18)
33. 小波分式滤波器
匡正,李云晖,崔明根
计算数学    1998, 20 (4): 353-358.   DOI: 10.12286/jssx.1998.4.353
摘要1215)      PDF(pc) (203KB)(795)    收藏
This paper gives the definition of wavelet fractional filter and presents the me thod of constructing wavelets by the fractional filter. This method not only incl udes Daubechies method which is used to construct wavelet by polynomial filter,but also includes the method of the filter of B-spline wavelet which is a special case of the fractional filter.
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被引次数: Baidu(7) CSCD(3)
34. 本征值有限元近似的一个抽象误差估计式
杨一都,石济民,林振宝,吕涛
计算数学    1998, 20 (4): 359-366.   DOI: 10.12286/jssx.1998.4.359
摘要1198)      PDF(pc) (229KB)(696)    收藏
In this paper an abstract error estimate theorem is given for finite element approximation of selfadjoint compact operators eigenvalue problems, and several new results are obtained by applying the theorem to conforming finite element method for second order elliptic problems, and mixed finite element method for the biharmonic problem.
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被引次数: Baidu(18) CSCD(7)
35. 解非线性方程的二阶敛速指数迭代法
吴新元
计算数学    1998, 20 (4): 367-370.   DOI: 10.12286/jssx.1998.4.367
摘要1648)      PDF(pc) (140KB)(1053)    收藏
A new iterative method-exponential iterative method of 2th order is proposed in this paper. The result is obtained by combining Liapunov's method with exponential approximation. Several numerial tests show the advantage of the method.
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被引次数: Baidu(56) CSCD(12)
36. 线性流形上矩阵方程AX=B的一类反问题及数值解法
廖安平
计算数学    1998, 20 (4): 371-376.   DOI: 10.12286/jssx.1998.4.371
摘要1235)      PDF(pc) (232KB)(586)    收藏
In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in [1, 2].
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被引次数: Baidu(53) CSCD(6)
37. 矩阵奇异值的下界估计
李竹香,逄明贤
计算数学    1998, 20 (4): 377-382.   DOI: 10.12286/jssx.1998.4.377
摘要1158)      PDF(pc) (211KB)(820)    收藏
In this paper, firstly we obtain an estimation of lower bounds for singular value of matrix, moreover give the equivalent representation of matrix when attaining estimation of lower bounds, these results improved corresponding results in [1]-[4].
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被引次数: Baidu(9) CSCD(1)
38. 用广义交互确认方法选择良好参数进行多元多项式散乱数据自然样条光顺
关履泰
计算数学    1998, 20 (4): 383-392.   DOI: 10.12286/jssx.1998.4.383
摘要1478)      PDF(pc) (353KB)(720)    收藏
By means of the theory of spline functions in Hilbert space, multivariate polynomial natural splines smoothing of scattered data are constructed without boundary conditions on certain bounded domains in R as a generalization of the well known uniariate natural polynomial splines smoothing. Generalized Cross-validation as a useful method for choosing a good ridge parameter of these multivariate smoothing splines is discussed. We give a available algorithm. Especialy an algorithm for bicubic splines smoothing is fairly easy to implement as example, and should be very useful in multivariate numerical analysis and signal analysis.
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被引次数: Baidu(8)
39. 空间圆柱螺旋线的NURBS表示
孙克豪
计算数学    1998, 20 (4): 393-402.   DOI: 10.12286/jssx.1998.4.393
摘要1208)      PDF(pc) (332KB)(728)    收藏
The paper is on the representation of a cylindrical helix by NURBS curves. A method is given, which discusses the influence on the shape of helix, produced by different ways of determining the positions of their control vertexes. The error distribution cases between the helix approximated by NURBS curves and the original theoretical one are also analyzed, and in the meanwhile a computation method is pointed out, which guarantees the requirements of precision.
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被引次数: Baidu(15) CSCD(2)
40. 稳定化有限元方法中逆估计常数的确定
段火元
计算数学    1998, 20 (4): 403-408.   DOI: 10.12286/jssx.1998.4.403
摘要1525)      PDF(pc) (270KB)(675)    收藏
A unified computable formula is presented for the constant of inverse estimation emanating from stabilized finite element methods. The method lies in introducing an elementwise bubble space spanned by the interpolation base functions with an additional bubble function given,and the parameter playing a stabilization role can take its value in a determined range.
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被引次数: Baidu(2)