中国科学院数学与系统科学研究院期刊网

计算数学 2001年 23卷

Please wait a minute...
选择: 显示/隐藏图片
1. 导数小片插值恢复技术与超收敛性
张铁
计算数学    2001, 23 (1): 1-8.   DOI: 10.12286/jssx.2001.1.1
摘要1095)      PDF(pc) (326KB)(767)    收藏
A derivative patch interpolating recovery technique is analyzed for the finite element interpolation operator of projection type and the two-point boundary value problems. It is shown that the convergence rate of the recovered derivative admits superconvergence on the recovered subdomain, and is two order higher than the optimal global convergence rate at each internal nodal point when even order finite element spaces and local uniform meshes are used.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(48) CSCD(4)
2. L_2逼近高精度格式的基本原理及其应用
苏铭德,李启兵,王筑
计算数学    2001, 23 (1): 9-26.   DOI: 10.12286/jssx.2001.1.9
摘要1117)      PDF(pc) (722KB)(663)    收藏
In the present paper, a new numerical method: L_2 approximation high accurate scheme is developed. The solution obtained by using this method satisfies not only at the discrete points, but also approximates to the exact solution in the total region. The basic principle is introduced and this method is used to solve some problems. The results show its high accuracy, high resolution and other advantages.
参考文献 | 相关文章 | 多维度评价
3. Pythagorean Bézier速端曲线及其等距线
韩西安,叶正麟,黄希利
计算数学    2001, 23 (1): 27-36.   DOI: 10.12286/jssx.2001.1.27
摘要1366)      PDF(pc) (357KB)(754)    收藏
The Pythagorean Bézier hodograph curves are Bézier curves {x(t), y(t)}, whose hodograph (first-order parametric derivative) components satisfy the Phythagorean condition x'2(t) +y'2(t) = σ'(t) for some polynomial σ(t). For nth degree PB curve (n is odd), its offset curve is represented by rational Bézier curve with (2n - 1)th degree and arc length by polynomial. Specially, the properties of cubic PB curve are studied, its geometric features are discussed and its quasi-Hermite interpolating curve and GC1 composite cubic PB curve are also constructed.
参考文献 | 相关文章 | 多维度评价
4. 解含非线性源项的变分不等式问题的非重叠区域分解法
李郴良,曾金平,周叔子
计算数学    2001, 23 (1): 37-48.   DOI: 10.12286/jssx.2001.1.37
摘要1141)      PDF(pc) (352KB)(691)    收藏
In this paper, a kind of nonoverlapping domain decomposition method, for solving variational inequalities with nonlinear source terms, is proposed. Convergence theorem and convergent rate analysis of the method are given.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(25) CSCD(2)
5. 基于非线性尺度不变性的CCG法
陈宁,桂卫华,李玉泉
计算数学    2001, 23 (1): 49-58.   DOI: 10.12286/jssx.2001.1.49
摘要1080)      PDF(pc) (342KB)(696)    收藏
In this paper, a conjugate-gradient method of invariancy to nonlinear scaling with respect to a conic function is proposed. This method may be used in the minimizer of a larger class of functions in a finite number of iterations, and this class of functions is more general than class of functions using the conjugate-gradient method of a conic function (to denote simply CCG)[1] to find its minimzer. In fact, this method is the extension of the CCG method. The results of the numerical evaluation show that the new method has a great effect.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(7)
6. 具简单界约束变分不等式的拟牛顿算法的收敛性分析
李董辉,杨余飞
计算数学    2001, 23 (1): 59-70.   DOI: 10.12286/jssx.2001.1.59
摘要1152)      PDF(pc) (476KB)(655)    收藏
We establish a quasi-Newton algorithm for solving a class of variational inequality problems which subproblems are linear equations. By presenting a suitable line search, the algorithm is well-defined. And under certain conditions, we get its global convergence and locally superlinear convergence.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(7)
7. 代数Riccati方程可稳解的条件数
刘新国
计算数学    2001, 23 (1): 71-80.   DOI: 10.12286/jssx.2001.1.71
摘要1169)      PDF(pc) (319KB)(689)    收藏
The Condition numbers are defined for the stabilizing Solutions of Continuoustime, discrete-time and the reverse discrete-time algebraic Riccati equations. The first-order perturbation expansions for the stabilizing Solutions are also obtained.
参考文献 | 相关文章 | 多维度评价
8. 调节熵函数法
杨庆之,杨德庄,张敏洪
计算数学    2001, 23 (1): 81-86.   DOI: 10.12286/jssx.2001.1.81
摘要1134)      PDF(pc) (237KB)(829)    收藏
In present paper, a modified maximum entropy method is proposed to solve minimax problem. This method is a generalization of well-known called maximum entropy method and attempts to overcome some drawbacks of former method. Some properties of new approximate function are presented first and then several numerical examples are given according to modified algorithm, which illustrates that our method is superior to former one.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(62)
9. 退化椭圆问题的最小二乘混合元逼近
陈艳萍,黄云清,沈祖和
计算数学    2001, 23 (1): 87-94.   DOI: 10.12286/jssx.2001.1.87
摘要1180)      PDF(pc) (261KB)(641)    收藏
We present a least-squares mixed finite element approximation of an elliptic problem with degenerate coefficients, arising in the study of the electronmagnetic field in a resonant structure with cylindrical symmetry. Optimal error estimates are developed, especially in the case of differing polynomial degrees for the primary solution approximation uh and the flux approximation σh.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(12)
10. 依赖时间的Lagrange乘子区域分解法的显式格式
刘金朝,梁国平,胡齐芽
计算数学    2001, 23 (1): 95-104.   DOI: 10.12286/jssx.2001.1.95
摘要1515)      PDF(pc) (368KB)(1050)    收藏

In the paper we introduce and study the explicit scheme of lagrangian multi- plier domain decomposition method dependent on time. The Uzawa algorithm is introduced to solve the interior displacement variables and the boundary multiplier variables. It will be shown that the condition number of the stiffness matrix of the lagrangian multiplier has a constant bound, i.e. O(1). The numerical experiments indicate that the method is very efficient.

参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(2)
11. 演化策略的全局收敛性
郭崇慧,唐焕文
计算数学    2001, 23 (1): 105-110.   DOI: 10.12286/jssx.2001.1.105
摘要1145)      PDF(pc) (249KB)(912)    收藏
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.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(129) CSCD(25)
12. 一类阻尼边界条件下的逆散射问题
刘继军
计算数学    2001, 23 (1): 111-120.   DOI: 10.12286/jssx.2001.1.111
摘要1100)      PDF(pc) (466KB)(717)    收藏
This paper considers the inverse scattering problem of an obstacle in R2 with impedance-type boundary. Our aim is to reconstruct the boundary impedance coefficient from the knowledge of scattered waves. For this ill-posed problem, we establish an effective inversion scheme to recover the unknown impedance in terms of the potential theory and optimal technique. Both convergence of the approximate solution and numerical example are presented.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(13) CSCD(2)
13. 再论求导数零点的二次收敛迭代法
王兴华,李冲
计算数学    2001, 23 (1): 121-128.   DOI: 10.12286/jssx.2001.1.121
摘要1281)      收藏
In this paper, we continues to study the convergent iteration method of order two given by the first author for finding zeros of the derivative. Under one global condition on the function, instead of two, the convergence determinations are established by using quadratic and cubical majorizing functions respectively.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(27) CSCD(1)
14. 一个刚性守恒律方程组的全隐式差分方法
汤华中
计算数学    2001, 23 (2): 129-138.   DOI: 10.12286/jssx.2001.2.129
摘要1302)      PDF(pc) (323KB)(750)    收藏
This paper is interested in a system of conservation laws with a stiff relaxation term arised in viscoelasticity. The properties of a class of fully implicit finite difference methods approximating this system are analyzed, which include maximum principles, bounds on the total variation, Ll-bounds, and L1-continuity estimates in term of some conserved physical quantity and this characteristic variables generated by difference schemes with proper initial data. These estimates are necessary for the existence of a bounded-total variation (BV) solution. Furthermore, we show that numerical entropy inequalities for some convex entropy pairs of the fully system hold.
参考文献 | 相关文章 | 多维度评价
被引次数: CSCD(1)
15. 数值求解延时微分方程的步长准则
丛玉豪,匡蛟勋
计算数学    2001, 23 (2): 139-144.   DOI: 10.12286/jssx.2001.2.139
摘要1296)      PDF(pc) (217KB)(894)    收藏
In this paper, we study the step criteria of numerical methods for delay differential equations, some results on step-length for Range - Kutta methods and linear multistep methods are given.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(7)
16. 由可逆线性系统确定的算子插值样条及其构造与连续性质
张新建
计算数学    2001, 23 (2): 145-154.   DOI: 10.12286/jssx.2001.2.145
摘要1317)      PDF(pc) (402KB)(703)    收藏
In this paper we investigate splines determined by certain linear operators defined in terms of system inverses. Best approximation properties for the proposed splines are given in an appropriate reproducing kernel Hilbert space framework, and the structual and continuity characteristics of these splines are obtained via the reduced-order system invese technique.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(2) CSCD(1)
17. 求解单调变分不等式问题的一类迭代方法
梁昔明,李飞
计算数学    2001, 23 (2): 155-162.   DOI: 10.12286/jssx.2001.2.155
摘要1271)      PDF(pc) (449KB)(827)    收藏
A class of iterative methods for solving monotone variational inequality problems are proposed. By solving strongly monotone variational inequality subproblems, the methods generate an iterative sequence which, for any starting point, converges to a solution of the variational inequality problem. Under suitable conditions, the convergence rate of the methods is given. Computational results are presented to show the stability and efficiency of the methods.
参考文献 | 相关文章 | 多维度评价
18. 带吸收边界条件的声波方程显式差分格式的稳定性分析
邵秀民,刘臻
计算数学    2001, 23 (2): 163-186.   DOI: 10.12286/jssx.2001.2.163
摘要1268)      PDF(pc) (727KB)(952)    收藏
It is well known that in numerical computations of wave equations by utilizing explicit schemes the stability is an extremely important problem when artifi- ctal boundaries are introduced and absorbing boundary conditions are imposed on them. In this paper, the stability of finite difference schemes for the acoustic wave equation with the first- and the second-order Clayton- Engquist - Majda absorbing boundary conditions is discussed by using energy techniques The corresponding stability conditions (i.e., the stability bounds of the CFL number) are given, which is sharper than those stability conditions for interior schemes or other kinds of boundary conditions. Numerical results are presented to confirm the correctness of the theoretical analysis.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(34) CSCD(3)
19. 三维热传导型半导体问题的交替方向特征有限元方法及理论分析
刘蕴贤
计算数学    2001, 23 (2): 187-198.   DOI: 10.12286/jssx.2001.2.187
摘要1198)      PDF(pc) (457KB)(748)    收藏
Alternating-direction methods are combined with characteristic finite element to treat the problem of three-dimensional transient behavior of semiconductor with heat-conduction, whose mathematical model is an initial and boundary problem of nonlinear partial differential equation system(Electric potential equation is approximated by mixed finite element method, concentration equations are approximated by alternating-direction characteristic finite element methods,and heatconduction equation is approximated by Galerkin alternating-direction method. Optimal order error estimates in L2 are demonstrated.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(9) CSCD(1)
20. 一维双曲守恒方程组的Taylor-Galerkin有限元方法
蔚喜军
计算数学    2001, 23 (2): 199-208.   DOI: 10.12286/jssx.2001.2.199
摘要1046)      PDF(pc) (326KB)(550)    收藏
In this paper, a numerical method is developed for solving one-dimensional hyperbolic system of conservation laws by the Taylor-Galerkin finite element method. The scheme is obtained by solving conservation equations associated HamiltonJacobi equations. The scheme has the TVD-like property under the uniform meshes. Numerical examples are given.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(9) CSCD(1)
21. 双对称非负定阵一类逆特征值问题的最小二乘解
廖安平,谢冬秀
计算数学    2001, 23 (2): 209-218.   DOI: 10.12286/jssx.2001.2.209
摘要1300)      PDF(pc) (321KB)(717)    收藏
In this paper, we consider the following two problems: Problem i. Given X ∈ Rmxn,A = diag(λ1,…, λm) > 0, find A E BSR such that where ||AX-X∧||=min, is Frobenius norm, BSR: is the set of all n x n bisymmetric nonnegative definite matrices. Problem Ⅱ. Given A* ∈ Rnxn, find ALS ∈ SE such that||A~*-A_(LS)||=inf||A~*-A|| where SE is the solution set of problem I. The existence of the solution for problem Ⅰ, Ⅱ and the uniqueness of the solution for Problem Ⅱ are proved. The general form of SE is given and the expression of ALS is presented.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(84) CSCD(7)
22. 对积分恒等式的一点补充和有限元的局部校正结果
朱起定,林群
计算数学    2001, 23 (2): 219-230.   DOI: 10.12286/jssx.2001.2.219
摘要1165)      PDF(pc) (363KB)(737)    收藏
In this paper, some notes for Lin's integral identity were given. forethermore, the local correction results for the finite element mehtod was obtained.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(2)
23. 再生核空间偏微分方程解析数值解
吴勃英
计算数学    2001, 23 (2): 231-238.   DOI: 10.12286/jssx.2001.2.231
摘要1325)      PDF(pc) (227KB)(545)    收藏
This paper gives a analytic solution of a boundary value problem of partial differential equation of the second order in the form of series on a reproducing kernel space H (D). This series solution possesses following characteristics:1. Truncating the series, the analytic numerical solution can be obtained. 2.when in creasing the number of the node, the error of the analytic numerical solution is monotone decreasing in the sense of the norm on HI(D) space.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(6)
24. 两步定常线性迭代法的收敛区域及最优参数选取
张玉海,朱本仁
计算数学    2001, 23 (2): 239-245.   DOI: 10.12286/jssx.2001.2.239
摘要1205)      PDF(pc) (213KB)(644)    收藏
In this paper we concern the convergence regions and the optimal parameters for linear second-degree stationary iterative methods applied to complex linear system with the help of the generalized Louts-Hurwitz's theorem. We show that the Chebyshev iteration is asymptotically equivalent to a linear second-degree stationary iteration. Finally some applications to CSOR and CMSOR are presented.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(3)
25. 非定常的热传导一对流问题的特征混合元法
罗振东,王烈衡
计算数学    2001, 23 (2): 246-256.   DOI: 10.12286/jssx.2001.2.246
摘要1216)      PDF(pc) (384KB)(726)    收藏
In this paper, a characteristic mined finite element method for the non stationary conduction-convection problems is presented. and the solvability and error estimates based on this method is derived.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(5)
26. 一个求解互补问题的光滑Newton方法
戚厚铎,张玉忠
计算数学    2001, 23 (3): 257-264.   DOI: 10.12286/jssx.2001.3.257
摘要1159)      PDF(pc) (268KB)(815)    收藏
A new smoothing Newton method was considered, its global convergence was established with comparasion to some other methods.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(42)
27. 一族多步二阶导数方法的收缩性
文立平,黄乘明
计算数学    2001, 23 (3): 265-270.   DOI: 10.12286/jssx.2001.3.265
摘要1209)      PDF(pc) (238KB)(847)    收藏
In this paper, a class of A (a)-contractive second derivative multistep methods for solving stiff ODE's is constructed, in comparison with the Enright method of the same order, the contractivity properties and the stability properties of the former are better than of the latter and the former preserves other advantages of the latter.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(11)
28. 按环路α-连对角占优阵及应用
李竹香,逄明贤
计算数学    2001, 23 (3): 271-278.   DOI: 10.12286/jssx.2001.3.271
摘要1151)      PDF(pc) (296KB)(824)    收藏
In this paper, the concept of a-connective diagonal dominant matrix according to circuit is introduced, and new conditions for H-matrices are obtained, corresponding results of [1]-[9] are improved and generalized.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(32) CSCD(3)
29. 一些矩阵分解的敏度分析
刘新国
计算数学    2001, 23 (3): 279-288.   DOI: 10.12286/jssx.2001.3.279
摘要1169)      PDF(pc) (265KB)(739)    收藏
This paper deals with the sensitivity analysis of the system Hessenberg form, the square reduced factorization of a Hamiltonian matrix, and the QT decomposition of a symplectic matrix. By local expansition, the condition numbers are defined.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(1)
30. 基于近似惯性流形的后验Galerkin的方法
黄艾香,刘之行,张引娣
计算数学    2001, 23 (3): 289-298.   DOI: 10.12286/jssx.2001.3.289
摘要1337)      PDF(pc) (399KB)(902)    收藏
In this paper, we give a new approximate inertial manifold and application to nonlinear elliptic boundary value problems. The approximate solution possesses over double convergence rate compared with the standard Galerkin approximate solution. And an example is given. The result of the numerical simulates show that the Post-Galerkin Method is very effective in improving precision of the ap- proximate solution.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(10) CSCD(1)
31. 求解一类非单调线性互补问题的路径跟踪法及其计算复杂性
何尚录,徐成贤
计算数学    2001, 23 (3): 299-306.   DOI: 10.12286/jssx.2001.3.299
摘要1375)      PDF(pc) (255KB)(694)    收藏
This paper presents a path-following method for a class of nonmonotonic linear complementary problems, and discusses its computational complexity.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(50) CSCD(7)
32. 求解约束优化问题的一个对偶算法
贺素香,张立卫
计算数学    2001, 23 (3): 307-320.   DOI: 10.12286/jssx.2001.3.307
摘要1199)      PDF(pc) (426KB)(944)    收藏
A dual algorithm based on the smooth function proposed by Polyak (1988), for solving nonlinear programming problems with inequality constraints, is presented. The local convergence of the dual algorithm is established and the convergence rate is estimated. Numerical results given in tall paper show that this dual algorithm is effective for solving inequality constrained optimization problems.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(21) CSCD(2)
33. 一个求解多维守恒律方程组的二阶显式有限元格式
应隆安,季晓梅,邓炯
计算数学    2001, 23 (3): 321-332.   DOI: 10.12286/jssx.2001.3.321
摘要1230)      PDF(pc) (501KB)(744)    收藏
We extend in this paper a second order fiuite element scheme, proposed by ourselves for unilti-dimensional scalar equations of conservation laws, to systems. The specific formulation of this scheme to ideal gas dynamic systems is also given. Resalts of numerical experiments are shown.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(6) CSCD(1)
34. 关于加法逆特征值问题
张玉海
计算数学    2001, 23 (3): 333-342.   DOI: 10.12286/jssx.2001.3.333
摘要1461)      PDF(pc) (327KB)(668)    收藏
It is proved that the additive inverse eigenvalue problem is equivalent to a polynomial system. By studying the system we obtain some new sufficient conditions on the solvabitity, and some numerical methods. Some numerical examples are presented.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(3)
35. Runge-Kutta方法关于时滞奇异摄动问题的误差分析
甘四清,孙耿
计算数学    2001, 23 (3): 343-356.   DOI: 10.12286/jssx.2001.3.343
摘要1501)      PDF(pc) (483KB)(878)    收藏
This paper is concerned with the error behaviour of Runge-Kutta methods ap- plied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimate of algebraically and diagonally stable Runge-Kutta methods with Lagrange interpolation procedure. Numerical experiments confirm our theoretical analysis.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(45) CSCD(1)
36. 三维Helmholtz方程外问题的自然边界元与有限元耦合法
贾祖朋,邬吉明,余德浩
计算数学    2001, 23 (3): 357-368.   DOI: 10.12286/jssx.2001.3.357
摘要1376)      PDF(pc) (429KB)(667)    收藏
In this Paper, a coupled natural boundary-finite element method is presented for solving three-dimensional Helmholtz equation in an unbounded domain.The existence and uniqueness of the solution for both continuous and discrete problems are studied.Error estimated and some numerical results are given.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(68) CSCD(3)
37. 复合材料弹性结构的高精度多尺度算法与数值模拟
刘晓青,曹礼群,崔俊芝
计算数学    2001, 23 (3): 369-384.   DOI: 10.12286/jssx.2001.3.369
摘要1413)      PDF(pc) (584KB)(990)    收藏
Multiscale asymptotic expansion for the solution of elastic structures of compos- ite materials is presented over general convex domains by constructing boundary layer properly. And the multiscale FE computing scheme and the post-processing technique with high accuracy are proposed. Finally, Numerical experiments sup- port strongly the theoretical results reported in this paper.
参考文献 | 相关文章 | 多维度评价
被引次数: CSCD(6)
38. W_2~m空间中样条插值算子与最佳逼近算子的一致性
张新建,黄建华
计算数学    2001, 23 (4): 385-392.   DOI: 10.12286/jssx.2001.4.385
摘要1305)      收藏
This paper discusses generalized interpolating splines which determined by n order linear differential operators, and the best operators of interpolating approximation in W_2~m spaces, The explicit constructive method for the reproducing kernel in W_2~m space is presented, and proves the uniformity of spline interpolating operators and the best operators of interpolating approximation W_2~m space by reproducing kernel. The explicit expression of approximation error on a bounded ball in W_2~m space, and error estimation of spline operator of approximation are obtained.
参考文献 | 相关文章 | 多维度评价
39. 改进HS共轭梯度算法及其全局收敛性
时贞军
计算数学    2001, 23 (4): 393-406.   DOI: 10.12286/jssx.2001.4.393
摘要1192)      PDF(pc) (432KB)(721)    收藏
This paper presents a modified HS conjugate gradient method for unconstrained optimization problem. The convergence of this algorithm is analyzed. Numerical experiments show that the algorithm is efficient by comparing with HS conjugate gradient method under Armijo line search.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(70) CSCD(15)
40. d维Bernstein算子加Jacobi权的收敛阶
曹飞龙,张学东
计算数学    2001, 23 (4): 407-416.   DOI: 10.12286/jssx.2001.4.407
摘要1299)      PDF(pc) (310KB)(663)    收藏
Using the equivalence relation between K-functional and moduli of smoothness, methods of partition function and induction, we establish a strong direct theorem and an inverse theorem of weak type of weighted approximation for d-dimensional Bernstein operators on a simplex in this paper.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(44) CSCD(3)