Generalized projection and approximation of fixed points of nonself maps

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T:K→E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T){xK: Tx=x}≠. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.     

Remarks on a Noble''''s Theorem

Noble proved the following Theorem: If A (?) X with a nonisolated point and B (?) Y, then A × B is bounded in X×Y if and only if the projection map π : X × Y → X is a z-map with respect to A × B and A, A is bounded in X and B is bounded in Y. In this note, we give two examples showing the necessary and sufficient conditions of Noble's theorem are not right.     

Galerkin Approximations for the Linear Parabolic Equation with the Third Boundary Condition

We solve a linear parabolic equation in ^d , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.     

完全Rees矩阵半群的分解及性质

用等价关系Q^~出了完全Rees矩阵半群的一种分解．而且得到了它的每个Q^~一类的表示．     

线性约束最优化的一个共轭投影梯度法

本结合共轭梯度法及梯度投影法的思想,建立线性等式约束最优化的一个新算法,称之为共轭投影梯度法。分别对二次凸目标函数和一般目标函数分析和论证了算法的重要性质和收敛性。     

EXTENDED OBLIQUE PROJECTION METHOD FOR GENERALIZED LEAST SQUARES PROBLEM

We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessary and sufficient conditions for computing the solution or the minimum N-norm solution of the min || A x- b ||M2 have been proposed as well.     

以系列三维立体投影实验为例谈大学物理实验中的创新型人才培养

创新能力是本世纪的核心竞争力,其关键是创新型人才的培养,这为理工类高校的实验教学提出了新的挑战.目前高校中的以学生为主体,教师为主导的大学生创新实验项目的实施是解决此挑战的有效途径之一.以笔者承担的系列三维立体投影物理实验的大学生创新实验项目为例,探讨了大学物理实验中的创新型人才培养模式.通过循序渐进的实验过程,引导学生自主搭建实验装置和编写控制程序,有效培养了学生的创新和实践能力,为高校实验教学改革提供了参考.     

基于自由曲面反射镜的低投射比超短焦投影物镜的光学设计

为了设计低投射比的超短焦投影物镜,本文采用自由曲面和折反式的光路结构设计了一种具有低投射比的超短焦投影物镜系统。该物镜由一个旋转对称的折射透镜组和一个自由曲面反射镜组成。采用11.938 mm的数字微镜器件(DMD)作为空间光调制器产生图像源。采用法线加权迭代优化的方法计算自由曲面。最后,分析了系统的性能。仿真结果表明:超短焦投影物镜可在580 mm的投影距离处实现3048 mm尺寸的大屏幕投影,系统的投射比低至0.19,系统的最大畸变小于0.72%。能够满足低投射比超短焦投影物镜的设计要求。该投影系统具有低投射比、低畸变、投影效果好等优点,可为超短焦投影系统的进一步发展提供有益参考。     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

根据表面反射特性进行目标探测的波段选择

计算和分析了表面反射特性对选择波段进行目标探测的影响.通过引入正交子空间投影方法,将背景信号从接收到的混合光谱中消除,从而达到压缩背景信号的目的.并在此基础上运用匹配跟踪算法自动地进行优化波段的选择,达到选择最佳波段的目的,从而进行目标探测.在大气外实际目标的探测中,得到了进行大气外目标探测的波段选择与目标表面反射特性的关系.