基于硬币实验的圆周率近似值计算

圆周率π的近似值计算,历史悠久,公式繁多.本文从硬币实验出发,运用数列极限知识让学生亲历体验π的近似值计算过程,领悟思想方法,感受数学魅力。     

Study on algorithm of dynamic uncalibrated eye-in-hand visual servoing system

Currently, most visual servoing system must be calibrated, while it is impossible to calibrate cameras and robot models precisely in industrial practice, so a novel dynamic uncalibrated eye-in-hand visual servoing system of tracking a moving target is proposed. The method does not require calibration of camera and robot kinematic models. Vision guided algorithm for tracking dynamic image is developed through minimizing nonlinear objective function. For the large residual has not been approximated in dynamic environment and the change of composite image Jacobian with time increment has not been computed in visual servoing system now,large residuals are dynamic approximated and the change of composite image Jacobian at each iterative step is computed. Simulation results demonstrate the validity of these approaches.     

基于MPS的任意变形蒙皮

针对利用MPS驱动的骨骼蒙皮动画对于非关节的对象精度不高的问题,提出了基于MPS的任意变蒙皮(SAD),该技术在任意动画上设置代理关节,自动为预先处理的任意动画的每一帧构建蒙皮相似量,利用二重四元数蒙皮,实验表明,SAD不仅能够有效地驱动非关节元素对象提高精度,而且能够充分利用MPS的优点.     

武器系统可靠性评估中的信息折合计算

基于贝叶斯理论，论述了将组成复杂系统各单元的可靠性信息折合成成败型单元信息，并进行信息综合计算，得出复杂系统可靠性评估结论的方法，并给出了算例。     

基于MPS的任意变形蒙皮

针对利用MPS驱动的骨骼蒙皮动画对于非关节的对象精度不高的问题，提出了基于MPS的任意变蒙皮（SAD），该技术在任意动画上设置代理关节，自动为预先处理的任意动画的每一帧构建蒙皮相似量，利用二重四元数蒙皮，实验表明，SAD不仅能够有效地驱动非关节元素对象提高精度，而且能够充分利用MPS的优点．     

浅析程序设计在解决与近似值相关的数学问题上的应用

本文将程序设计知识运用到求无理数的近似值、求解方程的近似根、求不规则图形面积等与近似值相关的数学问题上,让读者从新的角度审视求解与近似值相关的数学问题的新方法,并领悟程序设计在求解决这些数学问题上所显示出的优势。     

雷达角度分辨率

雷达角度分辨率(radar angular resolution)雷达在角度上，从毗邻目标的回波中．区分出各个目标信号的能力。通常以能区分出在相同距离、同样回波信号强度的二目标．所需的目标间最小方位角或仰角问题，来表示雷达的角度分辨率。雷达角度分辨率的数字度量的近似值为雷达天线波束的半功率点波束宽度。实际上由于二毗邻目标间相对相位关系不同，可获得的雷达角度分辨率的范围为1～2倍的天线波束半功率点间的宽度．典型值为1．5倍天线波束半功率点间的宽度。     

求多项式根的混合并行迭代法

本文给出一种求多项式根的混合并行迭代法，该方法由作者的方法与Durand-Kerner方法或Aberth方法构成，作者的方法是基于多项式根的分布理论的，该混合方法的收敛速度较快且没有初始近似值选取的麻烦。     

A New Weighted Least Squares Support Vector Machines and Its Sequential Minimal Optimization Algorithm

Least squares support vector machines （LSSVM） is widely used in pattern recognition and artificial intelligence domain in recent years for its efficiency in classification and regression. The solution of LSSVM is an optimization problem of a Sum squared error （SSE） cost function with only equality constraints and can be solved in a simple linear system. However, its generalization performance is sensitive to noise points and outliers that are often existent in training dataset. In order to endow robustness to LSSVM, a new method for computing weight vector of error is proposed and the substituting of weighted error vector for original error vector in LSSVM gives birth to a new weighted LSSVM. The method gets weight factor by computing distance between sample and its corresponding class center. Sequential minimal optimization （SMO） algorithm is also extended to the new method for its efficient application. Comparison experiments show superiority of the new method in terms of generalization performance, robust property and sparse approximation. Especially, the new method is much faster than the other method for large number of samples.     

The sharp upper bound on the distance between a parametric patch and its interpolated triangle

In computer aided geometric design （CAGD） and computer graphics, it is a general manipulation to approximate a surface by triangulation mesh. Thus a key problem is to estimate the error of the approximation. So far, many papers have given various estimate bounds of the distance between a parametric patch of a C2 surface and an arbitrary triangle whose vertices are on the patch, but these estimates are all imperfect, some of them have large error, some of them have complicated representation formulae. By using a succinct new method, a sharp upper estimate of the maximum distance between a patch and a triangle is obtained and a strict proof is given. This is very valuable for CAGD.