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| 1 | AN ANISOTROPIC NONCONFORMING FINITE ELEMENT WITH SOME SUPERCONVERGENCE RESULTS显示文摘The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis. | Dong-yangShi Shi-pengMao Shao-chunChen | 2005 | Journal of Computational Mathematics2005，23，3： | 184 |
| 2 | CONVERGENCE ANALYSIS FOR A NONCONFORMING MEMBRANE ELEMENT ON ANISOTROPIC MESHES显示文摘有限元素网孔的常规假设为常规一致元素 andnonconform-ing 元素两个都是有限元素近似的大多数分析的一个基本条件。这篇论文的目的是介绍处理一个四度的非一致的有限元素的近似的一条新奇途径因为第二在各向异性的网孔上订椭圆形的问题。没有在那里喉部的假设或伪制服假设的精力标准和 L2 标准的最佳的错误估计基于此处发现的这个元素的一些新特殊特征被获得。数字结果被给表明我们的理论分析的有效性。 | Dong-yang Shi Shao-chun Chen Ichiro Hagiwara | 2005 | Journal of Computational Mathematics2005，23，4： | 43 |
| 3 | AN ANISOTROPIC NONCONFORMING FINITE ELEMENT METHOD FOR APPROXIMATING A CLASS OF NONLINEAR SOBOLEV EQUATIONS显示文摘各向异性的 nonconforming 有限元素方法为非线性的 Sobolev 方程的一个班被介绍。最佳的错误估计和 supercloseness 为半分离、充分分离的近似计划被获得,它与传统的有限元素方法一样。另外,全球 superconvergence 通过 postprocessing 技术被导出。数字实验被包括说明建议方法的可行性。[从作者抽象] | Dongyang Shi Haihong Wang Yuepeng Du | 2009 | Journal of Computational Mathematics2009，27，2： | 49 |
| 4 | A NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION WITH MOVING GRIDS FOR STOKES PROBLEM显示文摘这篇论文被奉献给非与动人的格子遵守有限元素计划的五个参数因为速度压力在 2-D 混合了非静止的 Stokesproblem 的明确的表达。我们证明这个元素有各向异性的行为并且基于一些新奇技术在速度和压力的一些某些标准导出各向异性的错误评价。特别通过我们得到的小心的分析,一致性错误评价上的有趣的结果,它从来没被看见过为混合了有限元素方法在以前文学。 | Dong-yang Shi Yi-ran Zhang | 2006 | Journal of Computational Mathematics2006，24，5： | 33 |
| 5 | ON SPECTRAL METHODS FOR VOLTERRA INTEGRAL EQUATIONS AND THE CONVERGENCE ANALYSIS显示文摘这个工作的主要目的是为 Volterra 不可分的方程提供一条新奇数字途径基于一光谱途径。一个 Legendre 搭配方法被建议解决第二种类型的 Volterra 不可分的方程。如果内核函数和来源函数是足够地光滑的,我们为建议方法提供严密错误分析,它显示数字错误指数地腐烂。数字结果证实领带的理论预言集中的指数的率。在这个工作的结果似乎是第一成功光谱途径(与理论理由) 为 Volterra 类型方程。 | Tao Tang Xiang XU Jin Cheng | 2008 | Journal of Computational Mathematics2008，26，6： | 32 |
| 6 | A SELF-ADAPTIVE TRUST REGION ALGORITHM显示文摘In this paper we propose a self-adaptive trust region algorithm.The trust region radius is updated at a varable rate according to the ratio between the actual reduction and the predicted reduction of the objective function,rather than by simply enlarging or reducing the original trust region radius at a constant rate.We show that this new algorithm preserves the strong convergence property of traditional trust region methods.Numerical results are also presented. | Long Hei (Institute of Computational Mathematics and Scientific/Engineering Computing, Academy ofMathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China)(Department of Industrial Engineering and Management Sciences Northwestern University C2SO,2145 Sheridan Road Evanston, Illinois 60208, USA) | 2003 | Journal of Computational Mathematics2003，21，2： | 29 |
| 7 | ASYMPTOTIC ERROR EXPANSION AND DEFECT CORRECTION FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS显示文摘In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of Sobolev and viscoelasticity type equations. The global extrapolation and the correction approximations of third order, rather than the pointwise extrapolation results are presented. | Qun Lin Shu-hua Zhang Ning-ning Yan(Institute of Systems Science, Chinese Academy of Sciences, Beijing, China) | 1998 | Journal of Computational Mathematics1998，16，1： | 28 |
| 8 | A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS显示文摘Based on the work of paper,we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x)=0,where F(x):R^n→R^n is continuously differentiable and F'(x)is Lipschitz continuous.The algorithm is equivalent to a trust region algorithm in some sense,and the global convergence result is given.The sequence generated by the algorithm converges to the solution quadratically,if ||F(x)||2 provides a local error bound for the system of nonlinear equations.Numerical results show that the algorithm performs well. | Jin-yan Fan (Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China) | 2003 | Journal of Computational Mathematics2003，21，5： | 27 |
| 9 | CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION显示文摘In this paper we modify type approximate trust region methods via two curvilinear paths for unconstrained optimization. A mired strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. We give a series of properties of both optimal path and modified gradient path. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases. | De-tong Zhu (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China) | 2001 | Journal of Computational Mathematics2001，19，3： | 26 |
| 10 | NON-QUASI-NEWTON UPDATES FOR UNCONSTRAINED OPTIMIZATION显示文摘In this report we present some new numerical methods for unconstrained op-timization. These methods apply update formulae that do not satisfy the quasi-Newton equation. We derive these new formulae by considering different techniques of approkimating the objective function. Theoretical analyses are given to show the advantages of using non-quasi-Newton updates. Under mild conditions we prove that our new update formulae preserve global convergence properties. Numerical results are also presented. | YUAN, YX BYRD, RH | 1995 | Journal of Computational Mathematics1995，13，2： | 25 |
| 11 | MULTIVARIATE FOURIER SERIES OVER A CLASS OF NON TENSOR-PRODUCT PARTITION DOMAINS显示文摘This paper finds a way to extend the well-known Fourier methods,to so-called n+1 directions partition domains in n-dimension.In particular,in 2-D and 3-D cases,we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel paralleogram dodecahedron partitions,respectively.It has pointed that,the most concepts and results of Fourier methods on tensor-product case,such as periodicity,orthogonality of Fourier basis system,Partial sum of Fourier series and its approximation behavior,can be moved on the new non tensor-product partiton case. | Jiachang Sun(Parallel Computing Division, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China) | 2003 | Journal of Computational Mathematics2003，21，1： | 25 |
| 12 | CONSTRAINED QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENT显示文摘在这篇论文,我们基于非一致定义一个新非一致的四边的有限元素由在每个元素上强制限制的旋转 Q_1 元素,它有仅仅自由的三度。我们调查一致性,近似,超级靠近的性质,分离格林的功能和这个元素的超级集中。而且,我们建议一种 newpostprocessing 技术并且把它用于这个元素。帖子处理了分离答案,这被证明是超级的在网孔上的一个温和假设下面会聚。 | Jun Hu Zhong-ci Shi | 2005 | Journal of Computational Mathematics2005，23，6： | 24 |
| 13 | GENERALIZED DIFFERENCE METHODS ON ARBITRARYQUADRILATERAL NETWORKS显示文摘1.IntroductionConsidertheboundaryvalueproblemofthePoissonequationwherefiisaconvexpolygonregon;r^OfftheboundaryofOandf(x,y)aknownfunctiononfi.Thegeneralizeddifferencemethodsonquadrilateralnetworksforellipticequationsareproposedin[11],'wheretheconverge... | Yong-hai Li Rong-hua Li(Institute of Mathematics, Jinn University, Changchun 130023, China) | 1999 | Journal of Computational Mathematics1999，17，6： | 22 |
| 14 | ON HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHODS FOR CONTINUOUS SYLVESTER EQUATIONS显示文摘我们在场切开的 Hermitian 和 skew-Hermitian (HSS ) 为与 non-Hermitian 和积极 definite/semi-definite 矩阵解决大稀少的连续 Sylvester 方程的重复方法。HSS 重复方法的无条件的集中被证明,集中率上的上面的界限被导出。而且到计算花费了的还原剂,我们建立 HSS 重复方法的不精确的变体并且详细分析它的集中性质。数字结果证明 HSS 重复方法和它的不精确的变体是为连续 Sylvester 方程的这个类的有效、柔韧的解答者。[从作者抽象] | Zhong-Zhi Bai | 2011 | Journal of Computational Mathematics2011，29，2： | 22 |
| 15 | UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS显示文摘在这篇论文,我们认为 2D 和 3D Darcy 司烧连接问题。这些方程与 Brinkman 模型有关震颤两个 Darcy 是法律并且司烧在 PDE,但是与强烈不连续的粘性系数和 zeroth 顺序的一种单个形式的方程称为系数。我们在场构造一致地稳定的有限元素近似的三个不同方法。开始的二个方法基于 Darcy-Stokes-Brinkman 方程的原来的弱明确的表达。在我们考虑存在的第一个方法司烧元素。我们证明一个马厩司烧如果并且仅当分离地没有分叉的速度暗示几乎到处没有分叉的,元素关于系数和 Darcy-Stokes-Brinkman 方程的 jumps 也是一致地稳定的。在第二个方法,我们由修改遵守元素的一些著名 H (div ) 构造一致地稳定的元素。我们以一个统一方法给一些新 2D 和 3D 元素。在最后方法,我们与一个稳定术语修改 Darcy-Stokes-Brinkman 方程的原来的弱明确的表达。我们证明所有传统的马厩司烧元素在这新明确的表达下面关于系数和他们的 jumps 是一致地稳定的。 | Xiaoping Xie Jinchao Xu Guangri Xue | 2008 | Journal of Computational Mathematics2008，26，3： | 19 |
| 16 | GENERALIZED NEKRASOV MATRICES AND APPLICATIONS显示文摘In this paper,the concpet of generalized Nekrasov matrices in introduced,some prop-erties of these matrices are discussed,obtained equivalent representation of generalized diagonally dominant matrices. | Mingxian Pang Zhuxiang Li (Dept. of Math, of Normal college, Beihua University, Ji Lin 132013, China) | 2003 | Journal of Computational Mathematics2003，21，2： | 19 |
| 17 | THE SOLVABILITY CONDITIONS FOR THE INVERSE PROBLEM OF BISYMMETRIC NONNEGATIVE DEFINITE MATRICES显示文摘A = (aij) Rn is termed bisymmetric matrix if We denote the set of all n×n bisymmetric matrices by BSR. This paper is mainly concerned with solving the following two problems: Problem I. Given X, B E R, find A Pn such that AX = B, where Pn= {A E BSR }. Problem II. Given A* E R find A E SE such that where is Frobenius norm, and SE denotes the solution set of problem I. The necessary and sufficient conditions for the solvability of problem I have been studied. The general form of SE has been given. For problem II the expression of the solution has been provided. | Dong-xiu Xie Lei Zhang Xi-yan Hu | 2000 | Journal of Computational Mathematics2000，18，6： | 18 |
| 18 | NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS显示文摘This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs, are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method. | Cheng-jian Zhang(Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R. China) | 2002 | Journal of Computational Mathematics2002，20，6： | 18 |
| 19 | CASCADIC MULTIGRID FOR PARABOLIC PROBLEMSCASCADIC MULTIGRID FOR PARABOLIC PROBLEM显示文摘In this paper, we develop the cascadic multigrid method for parabolic problems. The optimal convergence accuracy and computation complexity are obtained. | Zhong-ci Shi, Xue-jun Xu (State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China) | 2000 | Journal of Computational Mathematics2000，18，5： | 18 |
| 20 | SUPERCONVERGENCE OF DG METHOD FOR ONE-DIMENSIONAL SINGULARLY PERTURBED PROBLEMS显示文摘集中和为在一个维的设定的一个不可思议地使不安的模型问题的不连续的 Galerkin (DG ) 方法的超级集中性质被学习。由与 DG 答案的适当地选择的数字踪迹,存在和唯一使用 DG 方法,最佳的顺序 L<sub>2</sub> 错误界限,和 2p +i 顺序数字踪迹斧子的超级集中建立了。数字结果显示 DG 方法不甚至在一致网孔下面生产任何摆动。数字实验证明在一致网孔下面,获得数字踪迹的一致超级集中似乎不可能。不过,对所谓的 Shishkin 类型的实现的感谢协调,一致 2p +1 顺序超级集中数字地被观察。 | Ziqing Xie Zhimin Zhang | 2007 | Journal of Computational Mathematics2007，25，2： | 18 |
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