不动点的单纯型算法

不动点理论是处理非线性问题的一个重要工具,非线性规划、数理经济学和其他应用领域中的许多问题都可归结为不动点问题,早在1912年,Brouwer就证明了著名的不动点定理,之后又有了Schauder、Kakutani等人的各种推广,但这些结果都是作为存在性定理(非构造方式)来处理问题的.直到十余年前才出现计算不动点的数值方法,从而形成了“不动点算法”这一迅速发展的数学新分支.第一代不动点算法是Scarf于1967年提出来的,他引进了所谓“本原集”的概念和“替代步骤的唯一性”,并利用Sperner引理和Brouwer不动点定理,得到了计算不动点近     

用单纯算法求解三解定理

在不动点的计算中,人们越来越注意单纯算法,特别是各种基于Brouwer不动点原理的定理,都可以有相应的单纯算法.本文讨论三解定理的单纯算法.§1介绍三解定理,它是由Amann最早提出的;§2介绍用单纯算法计算Brouwer不动点;§ 3考虑Amann三解定理的计算方案.     

不动点与平衡点

介绍Brouwer不动点定理、Kakutani不动点定理与数理经济学中平衡点和博弈论中Nash平衡点存在性定理的等价性结果.     

不动点与平衡点

介绍Brouwer不动点定理、Kakutani不动点定理与数理经济学中平衡点和博弈论中Nash平衡点存在性定理的等价性结果.     

二维Brouwer不动点定理的改进

<正> Brouwer不动点定理是拓扑学中一个著名的定理.特别,二维Brouwer不动点定理断言:若f是单位闭圆盘到自身的连续映射,则f必有不动点.即存在z∈,使得f(z)=z. 原条件不变,本文用较初等的方法将二维Brouwer不动点定理的结论改进为:对任     

欧氏空间自映射不动点算法与Brouwer不动点定理

本文给出计算欧氏空间连续自映射不动点的一种单纯同伦算法,并得到计算收敛的一个充分条件。著名的Brouwer不动点定理是上述充分条件的一个直接推论。     

不具单调性的均衡系统问题的解的存在性

该文引入并研究了一类不具单调性的均衡系统问题。利用Brouwer不定点定理，在有限维空间下得到了均衡系统问题的解的存在性。在无限维情形，通过引入函数族的(S)_{+-}条件，证明了基于(S)_{+-}条件下的均衡系统问题的解的存在性。     

一般化凸空间上的截口定理和变分不等式定理

摘要：本文利用Brouwer不动点定理或已知的KKM型定理，得到一般化凸空间上的截口定理．讨论了变分不等式解的存在性问题。对文中的相应结论进行了一般化和改进。     

Brouwer不动点定理的等价形式

一.引言和预备知识 Brouwer不动点定理是非线性分析和拓扑学中之一基本定理。半个多世纪以来,人们给出其多种形式的推广和多方面的应用。但是在本文中我们将要证明,截至目前Brouwer不动点定理的许多重要推广都是与之相等价的,而且都等价于集合的紧性。作为这一结果的应用,我们顺便部分解答了Smart所提出的一个公开问题。     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.