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A TRUST REGION METHOD FOR SOLVING DISTRIBUTED PARAMETER IDENTIFICATION PROBLEMS

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Journal of Computational mathematics 2003年第6期21卷 759-772页

作者： Yan-fei Wang Ya-xiang Yuan(LSEC, ICMSEC, academy of mathematics and system sciences, chinese academy of sciences,beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

This paper is concerned with the ill-posed problems of identifying a parameter in an elliptic equation which appears in many applications in science and industry. Its solution is obtained by applying trust region method to a nonlinear least squares error problem. Trust region method has long been a popular method for well-posed problems. This paper indicates that it is also suitable for ill-posed problems. Numerical experiment is given to compare the trust region method with the Tikhonov regularization method. It seems that the trust region method is more promising.

关键词： Parameter identification Ill-posed problems Trust region.

ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 2000年第3期18卷 313-324页

作者： Hua-zhong Tang (LSEC, Institute of Computational mathematics and Scientific /Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents a central relaxing scheme for scalar conservation laws. Details on the preliminary equations; Properties of the relaxed schemes; Conclusions.

关键词： hyperbolic conservation laws the relaxing scheme TVD cell entropy inequality

THE L^2-NORM ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT METHOD FOR THE 2ND ORDER ELLIPTIC PROBLEM WITH THE LOWEST REGULARITY

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Journal of Computational mathematics 2000年第3期18卷 277-282页

作者： Lie-heng Wang (LSEC, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents the abstract L...-norm error estimate of nonconforming finite element method. Use of the Aubin Nitsche Lemma in estimating nonconforming finite element methods; Details on the equations.

关键词： L-2-norm error estimate nonconforming f.e.m. lowest regularity

SOME NONLINEAR APPROXIMATIONS FOR MATRIX-VALUED FUNCTIONS

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Journal of Computational mathematics 2003年第6期21卷 801-814页

作者： Guo-liang Xu(academy of mathematics and system sciences, chinese academy of sciences,beijing 100080, china) academy of mathematics and system sciences Chinese Academy of Sciences 北京 100080

Some nonlinear approximants, i.e., exponential-sum interpolation with equal distance or at origin, (0,1)-type, (0,2)-type and (1,2)-type fraction-sum approximations, for matrix-valued functions are introduced. All these approximation problems lead to a same form system of nonlinear equations. Solving methods for the nonlinear system are discussed. Conclusions on uniqueness and convergence of the approximants for certain class of functions are given.

关键词： Matrix-valued function Nonlinear approximation Interpolation.

A CLASS OF NEW PARALLEL HYBRID ALGEBRAIC MULTILEVEL ITERATIONS

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Journal of Computational mathematics 2001年第6期19卷 651-672页

作者： Zhong-zhi Bai (LSEC ICMSEC, academy of mathematics and systems sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents preconditioning matrices having parallel computing function for the coefficient matrix and a class of parallel hybrid algebraic multilevel iteration methods for solving linear equations. Solution to elliptic ... 详细信息

关键词： elliptic boundary value problem system of linear equations symmetric positive definite matrix multilevel iteration parallel method

CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS

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Journal of Computational mathematics 2001年第5期19卷 539-548页

作者： Yu-hong Dai (LSEC, ICMSEC, academy of mathematics and systems sciences, chinese academy of sciences,beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents a study on methods for unconstrained optimization. Assumptions of the study; Main results; Convergence properties of the methods under simplified Armijo-type line search.

关键词： unconstrained optimization conjugate gradient (generalized) line search global convergence

MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE-Ⅱ SUPERCONDUCTORS

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Journal of Computational mathematics 1997年第4期15卷 365-384页

作者： Zhi-ming Chen (Institute of mathematics, chinese academy of sciences, beijing, china) 中科院数学所北京

In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2 and energy *** also report on some numerical results at the end of the paper.

关键词： Math QT MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE SUPERCONDUCTORS

Line bundles on non-primary Hopf manifolds

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Science china mathematics 2004年第4期47卷 538-551页

作者： LIU Weiming & ZHOU XiangyuInstitute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of mathematics, Zhejiang University, Hangzhou 310028, china Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Department of mathematics Zhejiang University Hangzhou China

Let X be a Hopf manifolds with Abelian fundamental group, L any flat line bundle on X, we give a formula for computing explicitly the cohomology Hq(X, Ωp(L) using the method of group action and the generalized Douady... 详细信息

关键词： Hopf surface, cohomology, line bundle, sections.

ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM

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Journal of Computational mathematics 2003年第4期21卷 481-490页

作者： Lie-heng Wang(LSEC, ICMSEC, academy of mathematics and system sciences, chinese academy of sciences,beijing 100080, china) academy of Mathemutics and system sciences Chinese Academy of Sciences LSEC ICMSECCAS 北京 100080

This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].

关键词： Obstacle problem Nonconforming finite element.