A lower bound on the performance of the quadratic discriminant function

The quadratic discriminant function is often used to separate two classes of points in a multidimensional space. When the two classes are normally distributed, this results in the optimum separation. In some cases however, the assumption of normality is a poor one and the classification error is increased. The current paper derives an upper bound for the classification error due to a quadratic decision surface. The bound is strict when the class means and covariances and the quadratic discriminant surface satisfy certain specified symmetry conditions.     

A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.

     

用迈克耳逊干涉仪测量气体折射率的误差的研究

研究在用迈克尔逊干涉仪测量气体折射率时存在的系统和方法误差，提出了误差修正方法。     

增长曲线模型中回归系数的广义根方估计

本文对增长曲线模型中的回归系数B提出了一种新的估计形式－广义根方估计的B（K），其中K＝diag(k1,k2,…，kp）并证明了通过广义根方偏参数ki(i=1,2,…，p）的适当选取可使得该估计在均方误差矩阵的意义下优于已有的LS估计和根方估计，及广义根方估计是可容许估计，本文还给出了选取广义根方偏参数的两种方法，算法及一个应用实例。     

人才招聘及评估模型的研究和实现

综述了互联网环境下人才招聘网站的应用现状，进而提出了面向政府及企事业单位选拔人才--站式服务的新思路；在给出了人才评估的分析模型后，对人才招聘及过滤进行了具体研究和实现．     

加速牛顿迭代收敛的新方法

提出了加速牛顿迭代收敛的新思想，构造出一类加权牛顿迭代格式，通过选取最优加权因子，使得该格式具有高阶收敛性和较小的渐近误差常数。     

UPWIND FINITE VOLUME SCHEMES FOR SEMICONDUCTOR DEVICE

The mathematical model of semiconductor devices is described by the initial boundary value problem of a system of three nonlinear partial differential equations. One equation in elliptic form is for the electrostatic potential; two equations of convection-dominated diffusion type are for the electron and hole concentrations. Finite volume element procedure are put forward for the electrostatic potential, while upwind     

离轴非球面轮廓测量导轨直线度误差补偿模型

由于研磨阶段非球面的面形误差将由几十微米收敛到几个微米,因此采用高重复精度的离散测量技术是决定误差收敛效率、影响加工进程的关键。在新一代数控光学加工中心(FSGJ Ⅱ)上,设计了双测头对非球面进行面形定量检测的轮廓测量机构。通过对测头运动导轨在x、z方向的直线精度的分析,建立了导轨直线度误差补偿模型,以较低的成本实现了较高的测量精度。     

Fourier regularization for a backward heat equation

In this paper a simple and convenient new regularization method for solving backward heat equation—Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.     

牛顿第二定律实验中的误差分析

本文是通过对加速度的实验值和理论值进行比较和分析，给出误差的合理范围。