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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

CONVERGENCE OF THE POINT VORTEX METHODS FOR EULER EQUATION ON HALF PLANE

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Journal of Computational mathematics 1996年第3期14卷 213-222页

作者： P.W. Zhang(department of mathematics, Beijing university, Beijing, China) BEIJING UNIV DEPT MATHBEIJING 100871PEOPLES R CHINA

In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition.... 详细信息

关键词： Math CONVERGENCE OF THE POINT VORTEX METHODS FOR EULER EQUATION ON HALF PLANE Zhang

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

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

Tree wavelet approximations with applications

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Science China mathematics 2005年第5期48卷 680-702页

作者： XU Yuesheng & ZOU Qingsong department of mathematics, Syracuse university, Syracuse, NY 13244, usa Institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China department of Scientific Computing and Computer Science, Zhongshan university, Guangzhou 510275, China 1. department of mathematics Syracuse University 13244 Syracuse NY USA 2. Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 3. department of Scientific Computing and Computer Science Zhongshan University 510275 Guangzhou China

We construct a tree wavelet approximation by using a constructive greedy scheme (CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.

关键词： greedy algorithms tree wavelet approximations Besov spaces.

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

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

Strong uniqueness of best approximations in spaces of bounded linear operators

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Science China mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu department of mathematics, Zhejiang university Hangzhou 310027, China department of mathematics, Zhejiang Normal university Jinhua 321004, China 1. department of mathematics Zhejiang University 310027 Hangzhou China 2. department of mathematics Zhejiang Normal University 321004 Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

AN ITERATION METHOD FOR INCOMPRESSIBLEVISCOUS/INVISCID COUPLED PROBLEM VIA A SPECTRALAPPROXIMATION

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Journal of Computational mathematics 1999年第4期17卷 379-396页

作者： Chuan-jn Xu(department of mathematics, Xiamen university, Xiamen 361005, China) 厦门大学数学系福建厦门 361005

An efficient iteration-by-subdomain method (known as the Schwarz alternating algorithm) for incompressible viscous/inviscid coupled model is presented. Appropriate spectral collocation approximations are proposed. The convergence analysis show that the iterative algorithms converge with a rate independent of the polynomial degree used.

关键词： coupled equations Navier-Stokes equations Euler equations cllocation approximation Schwarz alternating algorithm