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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

SYMPLECTIC COMPUTATION OF HAMILTONIAN systems (I)

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Journal of Computational mathematics 2002年第3期20卷 267-276页

作者： Yi-fa Tang(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

Presents information on a study which discussed a symplectic computation of hamiltonian systems. Terms of formal energy of mid-point rule; Analysis of the mathematical pendulum to test the convergence of the formal en... 详细信息

关键词： mid-point rule formal energy

ON THE CENTRAL RELAXING SCHEME Ⅱ: systems OF HYPERBOLIC CONSERVATION LAWS

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Journal of Computational mathematics 2001年第6期19卷 571-582页

作者： Hua-zhong Tang (School of Mathematical sciences, Peking University, beijing 100871, china) (lsec,icmsec academy of mathematics and systems sciences, chinese academy of sciences, beijing 100080, china) School of Mathematical sciences Peking University Beijing 100871 China

This paper continues to study the central relaxing schemes for system of hyperbolic conservation laws, based on the local relaxation approximation. Two classes of relaxing systems with stiff source term are introduced to approximate system of conservation laws in curvilinear coordinates. Based on them, the semi-implicit relaxing schemes are con- structed as in [6, 12] without using any linear or nonlinear Riemann solvers. Numerical experiments for one-dimensional and two-dimensional problems are presented to demon- strate the performance and resolution of the current schemes.

关键词： Hyperbolic conservation laws The relaxing system The central relaxing schemes The Euler equations.

A preconditioner for a kind of coupled FEM-BEM variational inequality

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science china mathematics 2010年第11期53卷 2811-2830页

作者： HU QiYa1 & YU DeHao2 lsec, icmsec, academy of mathematics and systems science, chinese academy of sciences, beijing 100190, china 1. lsec ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

In this paper we are concerned with a kind of nonlinear transmission problem with Signorini contact conditions. This problem can be described by a coupled FEM-BEM variational inequality. We first develop a preconditioning gradient projection method for solving the variational inequality. Then we construct an effective domain decomposition preconditioner for the discrete system. The preconditioner makes the coupled inequality problem be decomposed into an equation problem and a "small" inequality problem, which can be solved in parallel. We give a complete analysis to the convergence speed of this iterative method.

关键词： Signorini contact FEM-BEM coupling variational inequality preconditioning gradient projection preconditioner condition number

Study on the generator f of the operators I_n and I_t

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science china mathematics 2010年第10期53卷 2589-2603页

作者： CHEN HanLin academy of mathematics and systems science,chinese academy of sciences,beijing 100190,china 1. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100190 China

Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s *** call f the generator of the operators In and *** is well known that there are many results on operators In and *** there remain some important problems to be further *** application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative *** this paper,we focus on the available generator in the class of spline *** shall see that not all spline functions can be used to construct available ***,we do find a spline function in S,of degree m-1,where m is even and S is a class of *** for odd m the problem is still *** on spline functions in this paper are new.

关键词： generator available generator inner product operator spline interpolation operator two-closed refinable

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) lsec ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

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.

Holomorphic invariant forms of a bounded domain

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science china mathematics 2008年第11期51卷 1945-1964页

作者： LU QiKeng Institute of mathematics, academy of mathematics and systems science, chinese academy of sciences, beijing 100190, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Given a complete ortho-normal system ? = (?0,?1,?2,…) of L 2 H( $ \mathcal{D} $ ), the space of holomorphic and absolutely square integrable functions in the bounded domain $ \mathcal{D} $ of ? n , we construct a holomorphic imbedding $ \iota _\phi :\mathcal{D} \to \mathfrak{F}(n,\infty ) $ , the complex infinite dimensional Grassmann manifold of rank n. It is known that in $ \mathfrak{F}(n,\infty ) $ there are n closed (μ, μ)-forms τμ (μ = 1,…,n) which are invariant under the holomorphic isometric automorphism of $ \mathfrak{F}(n,\infty ) $ and generate algebraically all the harmonic differential forms of $ \mathfrak{F}(n,\infty ) $ . So we obtain in $ \mathcal{D} $ a set of (μ, μ)-forms ι ? * τμ (μ = 1,…, n), which are independent of the system ? chosen and are invariant under the bi-holomorphic transformations of $ \mathcal{D} $ . Especially the differential metric ds 2 1 associated to the K?hler form ι ? * τ1 is a K?hler metric which differs from the Bergman metric ds 2 of $ \mathcal{D} $ in general, but in case that the Bergman metric is an Einstein metric, ds 1 2 differs from ds 2 only by a positive constant factor.

关键词： complete ortho-normal system holomorphic invariant forms 32A36 32A65

The reason of Hopf’s and Oleinik’s proofs for countability of shocks being wrong

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science china mathematics 2012年第4期55卷 727-729页

作者： LI BangHe academy of mathematics and systems science,chinese academy of sciences,beijing 100190,china 1. academy of mathematics and systems science Chinese Academy of Sciences Beijing 100190 China

For the number of complete shock curves of a conservation law with one space variable,Hopf in 1950 for the Burger equation,and Oleinik in 1956 for the general,stated that it is at most *** 1979,the present author published an example to show that the statement of Hopf and Oleinik is *** after so long time,the wrong statement for countability still appeared in some publications,which is at least partly due to that some ones felt difficult to understand Hopf and Oleinik’s proofs being ***,pointing out where they went wrong becomes very necessary.

关键词： countability of shocks uncountability of shocks conservation law