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A GOLDSTEIN'S TYPE PROJECTION METHOD FOR A CLASSOF VARIANT VARIATIONAL INEQUALITIES

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Journal of Computational mathematics 1999年第4期17卷 425-434页

作者： Bing-sheng He(department of mathematics, Nanjing university, Nanjing 210008, china) department of mathematics Nanjing University Nanjing 210008 China

Some optimization problems in mathematical programming can be translated to a variant variational inequality of the following form: Find a vectoru*, such that This paper presents a simple iterative method for solving this class of variational inequalities. The method can be viewed as an extension of theGoldstein's projection method. Some results of preliminary numerical experiments are given to indicate its applications.

关键词： Variational inequality Goldstein projection method.

ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (department of mathematics, East china Normal university, Shanghai 200062, china) E china Normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.

关键词： matrix unitarily invariant norm condition number

THE CONVERGENCE ON A FAMILY OF ITERATIONS WITH CUBIC ORDER

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Journal of Computational mathematics 2001年第5期19卷 467-474页

作者： Dan-fu Han (department of mathematics, Zhejiang university, Hangzhou 310028, china) 浙江大学浙江杭州 310028

Establishes a convergent theorem for a family of iterations with cubic order by using general convergence hypotheses. Disadvantage of using the cubic majorizing function; Convergence of the majorizing sequence; Overvi... 详细信息

关键词： convergence majorizing method gamma-condition error estimate

DISTURBANCE ATTENUATION FOR UNCERTAIN NONLINEAR CASCADED SYSTEMS

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Journal of Systems Science & Complexity 2004年第3期17卷 318-324页

作者： BIWeiping MUXiaowu SUNYuqiang departmentofmathematics HenanNormalUniversityXinxiang453007China departmentofmathematics ZhengzhouUniversityZhengzhou450052China departmentofComputerScience HenanNormalUniversityXinxiang453007China

In present paper, the disturbance attenuation problem of uncertain nonlinear cascaded systems is studied. Based on the adding one power integrator technique and recursive design, a feedback controller that solves the ... 详细信息

关键词： uncertain nonlinear systems disturbance attenuation

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

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Journal of Computational mathematics 2000年第1期18卷 1-12页

作者： Bing-sheng He(department of mathematics, Nanjing university, Naming 210093, china) 南京大学江苏南京 210093

Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t... 详细信息

关键词： trust region problem conjugate gradient method projection and contraction method

THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 401-408页

作者： LIU TAISHUN (department of mathematics, university of Science and Technology of china, Hefei 230026, china)REN GUANGBIN (department of mathematics, university of Science and Technology of china, Hefei 230026, china) Univ Sci & Technol china Dept Math Anhua 230026 Peoples R China

The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular *** type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent *** theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.

关键词： Starlike mappings Growth theorem Starlike circular domains

GENUINE-OPTIMAL CIRCULANT PRECONDITIONERS FOR WIENER-HOPF EQUATIONS

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Journal of Computational mathematics 2001年第6期19卷 629-638页

作者： Fu-rong Lin (department of mathematics, Shantou university, Shantou 515063,china) 汕头大学广东汕头 515063

Discusses the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. Definition of the genuine-optimal circulant preconditioner; Use of the preconditioned conjugate gradient method; Numeric... 详细信息

关键词： Wiener-Hopf equations circulant preconditioner preconditioned conjugate gradient method quadrature rules Hilbert-Schmidt norm

ON THE MODULI NUMBER OF PLANE CURVE SINGULARITIES WITHONE CHARACTERISTIC PAIR

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Chinese Annals of mathematics,Series B 1999年第4期20卷 407-412页

作者： CHEN HAO(department of mathematics, Zhongshan university, Guangzhou 510275, china) Zhongshan Univ Dept Math Guangzhou 510275 Peoples R China

The author gives another linear-algebraic proof of the famous result of Zariski, Delorme,Briancon- Granger- Maisonobe about the moduli number of plane curve singularities with the same topological type as Xa + Yb = 0 (i.e.,with one characteristic pair). Since the original proof depends very much on the division theorem of Briancon, it cannot be generalized to higher dimensions. It is hopeful that the proof here will be applied to the higher dimensional cases.

关键词： Moduli number Plane curve Singularity Characteristic pair

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

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Chinese Annals of mathematics,Series B 1999年第4期20卷 473-478页

作者： MENG ZAIZHAO(department of mathematics, Peking university, Beijing 100871, china) Peking Univ Dept Math Beijing 100871 Peoples R China

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2). It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3 integers n ≤x.

关键词： Divisor function Multiplicative function Congruence