Polynomial approximation of functions of matrices and applications

In solving a mathematical problem numerically, we frequently need to operate on a vector by an operator that can be expressed asf(A), whereA is anN ×N matrix [e.g., exp(A), sin(A), A^–-]. Except for very simple matrices, it is impractical to construct the matrixf (A) explicitly. Usually an approximation to it is used. This paper develops an algorithm based upon a polynomial approximation tof (A). First the problem is reduced to a problem of approximatingf (z) by a polynomial in z, where z belongs to a domainD in the complex plane that includes all the eigenvalues ofA. This approximation problem is treated by interpolatingf (z) in a certain set of points that is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problems is described. Since a solution to a linear systemAx=b isx=A ^–1 b, an iterative solution algorithm can be based upon a polynomial approximation tof (A)=A ^–1. We give special attention to this important problem.     

基于偏微分的图像放大算法研究

在研究图片放大算法中,分析了现有的运用偏微分算法在图像法大中的不足,利用图像放大过程中的边缘信息可预知性,本文提出一种新的基于偏微分方程的图像放大算法,这种算法通过将图像边缘检测、平滑处理,然后采用三次样条插值算法对边缘进行相应倍数的放大,并通过对可能出现的锯齿边缘进行细化处理;将处理过的边缘作为放大图像的边缘,从而可以将源图像的边缘很好的保持下来,避免了偏微分方程放大过程中出现的边缘模糊现象。实验结果显示,该方法是一种能够很好的保存图像的边缘信息的图像放大算法。     

三次样条构造的伪逆解法

为了提高三次样条构造的可行性, 基于矩阵的伪逆方法, 提出一种不依赖额外约束条件的三次样条构造的伪逆解法。该解法通过求解出三次样条二阶导数的最小范数解, 从而较好地构造出三次样条函数。理论分析及数值实验结果表明该三次样条构造的伪逆解法具有简单、有效等特点。综合分析各种构造解法的性质, 对各种三次样条构造解法进行归类比较, 为在实际工程计算应用中选择合适的三次样条构造解法提供了指导方向。     

基于SOPC的高精度超声波温度计设计

根据在介质中超声波的传播速度随温度变化而变化的特点为设计原理,以基于Nios II处理器软核的可编程系统级芯片(SOPC)为控制核心,设计了高精度超声波温度计。在SOPC上同时实现了高频信号发生器模块、高速信号电路控制模块、信号自动采集控制模块以及Nios II软核处理器模块,缩小了体积,并降低了成本。传播时间的精确测量采用软件细分插补算法,经过理论分析和实验验证,该方法能够达到ns级超声波传播时间的测量,使设计的超声波温度计能够实现分辨率优于0.001℃的温度测量。     

等离子硅刻蚀及其工艺参数的多尺度优化

用CFD-ACE+和CFD-TOPO分别对容性耦合等离子体反应腔室放电和等离子硅刻蚀过程进行仿真,讨论不同射频电压和腔室条件对等离子体特性的影响.结果表明:随着射频电压的升高,离子的通量增大;在低射频电压时,离子通量随腔室压强的升高而减小,而在高射频电压时趋势则相反.用Kriging模型对影响刻蚀形貌的参数(腔室压强和射频电压)进行优化,结果表明该优化方法可以为工艺条件相近的刻蚀机设备的设计提供参考.     

The Cerebellum according to the Ouroboros Model,the ＂Interpolator Hypothesis＂

The Ouroboros Model offers a novel cognitive architecture with an algorithmic backbone of iterative and self-referential processing. All memory content is organized into meaningful pieces of data, i.e.,chunks and schemata, which are laid down as a kind of snapshots of all activations at a relevant point in time. This entails a grainy structure of memory content. Whereas a core process of ＂consumption＂ analysis can naturally be defined taking advantage of this parcellation, it necessitates interpolation for fine nuances, especially for the representation of intermediate values during transients. It is argued that, in the vertebrate brain, essential interpolation functionality is provided by the cerebellum. Findings concerning movement control and perception as well as the involvement of the cerebellum in more abstract, cognitive, tasks can be interpreted as reflecting a function of the cerebellum as a co-processor, i.e., a general-purpose interpolator. The cerebellum is thus boosting representations in cerebral cortex areas, which are reciprocally connected with cerebellar cortex areas. In this paper, it is sketched how the new ＂interpolator hypothesis＂ can explain manifold observations, effectively subsuming previous theories of the function of the cerebellum. Directly relating to the BICA challenge, a general-purpose interpolator is postulated as an efficient device providing fine-grained resolution for the representation of diverse content, potentially useful in any cognitive architecture.     

广角摄像机在机器人视觉定位中的应用

为了保证广角摄像机在现代机器人视觉定位应用中的准确性,以广角摄像机像素坐标的反畸变过程为研究对象,提出一种在畸变对应表的基础上使用中心迭代法以及区域插值法确定物体实际位置的方法。通过实验证明了该方法能够测量物体的位置,其精度能够满足工业使用要求。     

改进的局域均值分解在机械故障诊断中的应用

为了准确地提取出故障特征,把局域均值分解算法应用于机械故障振动信号的特征提取中.然而在对信号进行局域均值分解时,由于端点的趋势无法预知,在分解时会污染到整个信号序列,而且滑动平均造成了信号的过平滑处理,导致故障特征不能准确地提取.采用波形匹配解决端点处信号的走势,之后再利用线性插值求得信号的局域均值函数与包络函数,通过在Matlab环境下仿真调幅信号验证了该算法在端点处能很好的保持原有信号的特征;并采用实际的机械振动信号进行实验验证,引入端点效应评价指标,根据分解后的生产函数与原信号的相关系数验证了改进的局域均值分解更能准确地提取故障特征.