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THE PRIMAL-DUAL POTENTIAL REDUCTION ALGORITHM FOR POSITIVE SEMI-DEFINITE PROGRAMMING

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Journal of Computational mathematics 2003年第3期21卷 339-346页

作者： Si-ming Huang(Institute of Policy and Management, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) Institute of Policy and Management Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.

关键词： Positive semi-definite programming Potential reduction algorithms Complexity.

PROBABILISTIC NUMERICAL APPROACH FOR PDE AND ITS APPLICATION IN THE VALUATION OF EUROPEAN OPTIONS

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Journal of Computational mathematics 2001年第6期19卷 591-600页

作者： Dong-sheng Wu (Institute of systems Science, academy of mathematics and systems sciences, chinese academy of sciences, beijing 100080, china ) 中科院系统科学所北京 100080

Presents a probabilistic numerical approach for a class of probabilistic differential equation. Application of the Brownian motion and Monte-Carlo method; Application in the valuation of European Options.

关键词： Brownian motion probabilistic numerical solution European Options

Central simple Poisson algebras

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Science china mathematics 2004年第2期47卷 245-263页

作者： SU Yucai & XU XiaopingDepartment of mathematics, Shanghai Jiaotong University, Shanghai 200030, china Institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of mathematics Shanghai Jiaotong University Shanghai China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic *** Lie algebra structures of these Poisson algebras are in general not finitely-graded.

关键词： Poisson algebra, locally-finite operator, derivation, finitely-graded, isomorphism class.

ON THE ERROR ESTIMATE OF LINEAR FINITE ELEMENT APPROXIMATION TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

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Journal of Computational mathematics 2000年第6期18卷 561-566页

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

In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h[sup ?]) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while *** et. al. Obtained the error bound O(h[sup ?]) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]). [ABSTRACT FROM AUTHOR]

关键词： contact problem finite element approximation

The Koppelman-Leray formula on complex Finsler manifolds

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Science china mathematics 2005年第6期48卷 847-863页

作者： QIU Chunhui & ZHONG Tongde School of Mathematical sciences, Xiamen University, Xiamen 361005, china academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china School of Mathematical sciences Xiamen University Xiamen China academy of mathematics and system sciences Chinese Academy of Sciences Beijing China

By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.

关键词： complex Finsler manifold, Chern-Finsler connection, invariant integral kernel, Koppelman-Lerayformulas, - -equation.

Transcendence of Certain Trigonometric Series

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Acta Mathematica Sinica,English Series 2002年第3期18卷 481-488页

作者： Yao Chen ZHU academy of mathematics and system sciences. The chinese academy of sciences, beijing 100080. P. R. china academy of mathematics and system sciences The Chinese Academy of Sciences Beijing P. R. China

In this paper the transcendence of values of certain trigonometric series with algebraic coefficients and its derivatives at algebraic points is proved under a general condition dependent only on the coefficients. The... 详细信息

关键词： Transcendence Trigonometric series Linear independence Number field

Poisson kernel and Cauchy formula of a non-symmetric transitive domain

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Science china mathematics 2010年第7期53卷 1678-1683页

作者： LU Qi-Keng Institute of mathematics, academy of mathematics and system Science, chinese academy of sciences, beijing 100190, china Institute of mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing China

In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2 ∈Cq×m|2i1( Z-Z+)-Z1Z1′-Z2′Z2>0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S m,p,q is not symmetric. However the map T0:Z→Z, Z1→Z1 , Z2→Z2 transforms S m,p,q into a domain S I (m, m + p + q) which can be mapped by the Cayley transformation into the classical domains R I (m, m + p + q). The pull back of the Bergman metric of R I (m, m + p + q) to S m,p,q is a Riemann metric ds 2 which is not a Khler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator associated with the metric ds 2 when it acts on the Poisson kernel of S m,p,q equals 0. Consequently, the Cauchy formula of S m,p,q can be obtained from the Poisson formula.

关键词： Poisson kernel Cauchy formula

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ON KORN'S INEQUALITY

Journal of Computational mathematics 2003年第3期21卷 321-324页

作者： Lie-heng Wang(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 devoted to give a new proof of Korn's inequality in LT - norm (1 < γ < ∞).

关键词： Korn's inequality.

Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch

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Acta Mathematicae Applicatae Sinica 2003年第1期19卷 19-24页

作者： Da-chuan XuInstitute of Applied mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Institute of Applied mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the ... 详细信息

关键词： Keywords Quasi-Newton method Broyden class non-monotone linesearch global convergence unconstrained optimization